Louis Jeanjean

Professor - Université de Franche-Comté

Laboratoire de Mathématiques
UMR CNRS 6623
Université de Franche-Comté
16 route de Gray
25030 Besançon Cedex

Research Team  : Partial Differential Equations

Bâtiment métrologie, bureau 424 B
Tél : +33 (0)3 81 66 64 66
Fax : +33 (0)3 81 66 66 23
louis.jeanjean univ-fcomte.fr

Editorial Activities  : Member of the Editorial board of Advances in Nonlinear Analysis.

Research interests  :

• Nonlinear elliptic equations
  

• Minimax methods in the calculus of variations
  

• Homoclinics and heteroclinics solutions for Hamiltonian systems
  

• Bifurcation from the essential spectrum
  

• Existence and multiplicity of peak solutions
  

PhD students  :

• Stefan Le Coz, defense in 2007 (Maître de conférences, University of Toulouse, France)

• Tingjian Luo, defense in 2013 (Associate Professor Guangzhou University, China)

• Tianxiang Gou, defense in 2017 (Assistant Professor, Xi’an Jiaotong University, China).

• Antonio Fernandez Sanchez, defense in 2019 (Tenure track, Universidad Autonoma de Madrid). Co-direction with C. De Coster

• Thanh Trung Le, defense in 2022 (Postdoc - UFC with Raluca Eftimie).

• Pablo Carrillo, start of the PhD in 2022

Lists of publications

• [1] Buffoni B. and Jeanjean L., Bifurcation from the essential spectrum towards regular values, J. Reine Angew. Math., 445, 1993, 1-29.

• [2] Buffoni B. and Jeanjean L., Minimax characterisation of solutions for a semi-linear elliptic equation with lack of compactness, Ann. Inst. H. Poincaré, Anal. non-lin., 10, 1993, 377-404.

• [3] Buffoni B., Jeanjean L. and Stuart C.A., Existence of a non-trivial solution to a strongly indefinite semilinear equation , Proc. A.M.S., 119, 1993, 179-186.

• [4] Jeanjean L., Solution in spectral gaps for a nonlinear equation of Schrödinger type , J. Diff. Eqs., 112, 1994, 53-80.

• [5] Jeanjean L., Approche minimax des solutions d’une équation semi-linéaire elliptique en l’absence de compacité, Ph. D. Thesis, EPFL, Lausanne, 1992.

• [6] Jeanjean L., Existence of connecting orbits in a potential well, Dyn. Sys. Appl., 3, 1994, 537-562.

• [7] Giannoni F., Jeanjean L. and Tanaka K., Homoclinic orbits on non-compact Riemannian manifolds for second order Hamiltonian systems, Rend.Sem. Mat. Univ. Padova, 3, 1995, 153-176.

• [8] Bertotti M.L. and Jeanjean L., Multiplicity of homoclinic solutions for singular second order conservative systems, Proc. Roy. Soc. Edinburgh, 128 A, 1996, 1169-1180.

• [9] Jeanjean L., Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Analysis TMA, 28, 1997, 10, 1633-1659.

• [10] Jeanjean L., Two positive solutions for a class of nonhomogeneous elliptic equations, Diff. Int. Eqs., 10, 1997, 609-624.

• [11] Caldiroli P. and Jeanjean L., Homoclinics and Heteroclinics for a class of conservative singular Hamiltonian systems, J. Diffs. Eqs., 136, 1997, 76-114.

• [12] Jeanjean L.,On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer type problem set on R^N, Proc. Roy. Soc. Edinburgh A, 129, 4, 1999, 787-809.

• [13] Jeanjean L. and Toland J.F., Bounded Palais-Smale Mountain-Pass sequences, C. R. Acad. Sci. Paris, t. 327, 1, 1998, 23-28.

• [14] Jeanjean L., Local conditions insuring bifurcation from the continuous spectrum, Math. Z.,232, 4, 1999, 651-664.

• [15] Giacomoni J. and Jeanjean L., A variational approach to bifurcation into spectral gaps, Ann. Scu. Norm. Sup. Pisa, C. Sci., 28, 4, 1999, 651-674.

• [16] Alessio F., Jeanjean L. and Montecchiari P., Stationary layered solutions in R^2 for a class of non-autonomous Allen-Cahn equations, Calc. Var. Part. Diff. Equa., 11, 2, 2000, 177-202.

• [17] Jeanjean L., Méthodes variationnelles et applications à quelques problèmes d’analyse nonlinéaire, Mémoire d’habilitation, Université de Marne-la-vallée, février 1999.

• [18] Alessio F., Jeanjean L. and Montecchiari P.,Existence of infinitely many stationary layered solutions in R^2 for a class of periodic Allen-Cahn equations, Comm. Partial Diff. Equa., 27, 7-8, 2002, 1537-1574.

• [19] Jeanjean L. and Tanaka K., A positive solution for an asymptotically linear elliptic problem on R^N autonomous at infinity, ESAIM Control Optim. Calc. Var., 17, 2002, 597-614.

• [20] Jeanjean L. and Tanaka K., A remark on least energy solutions in R^N, Proc Amer. Math. Soc, 131, 2003, 2399-2408.

• [21] Jeanjean L. and Tanaka K.,A note on a mountain pass characterization of least energy solutions, Adv. Non. Studies, 3, 2003, 445-455.

• [22] Colin M. and Jeanjean L., Solution for a quasilinear Schrödinger equation : a dual approach, Nonlinear Analysis, 56, 2004, 213-226.

• [23] Jeanjean L. and Tanaka K., Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities, Calc. Var. Partial Diff. Equations., 21, 2004, 3, 287-318.

• [24] Jeanjean L. and Tanaka K.,A positive solution for a nonlinear Schrödinger equation on R^N, Indiana Univ. Journal, 54, 2, 2005, 443-464.

• [25] D’avila A. and Jeanjean L.,A result on singularly perturbed elliptic problems, Comm. Pure App. Anal, 4, 2, 2005, 343-358.

• [26] Jeanjean L., Problèmes elliptiques non linéaires, cours préparé à l’occasion de l’école d’été de Grenoble en juin 2005.

• [27] Jeanjean L. and Le Coz S.,An existence and stability result for standing waves of nonlinear Schrödinger equations, Advances in Differential Equations, 11, 7, 2006, 813-840.

• [28] Byeon J. and Jeanjean L., Standing waves for nonlinear Schrödinger equations with a general nonlinearity, Archives for Rational Mechanics and Analysis, 185, 2, 2007, 185-200. See also [33].

• [29] Ding Y. and Jeanjean L., Homoclinic orbits for a non periodic Hamiltonian system, Journal of Differential Equations 237, 2, 2007, 473-490.

• [30] Byeon J. and Jeanjean L.,Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity, Discrete and continuous dynamical systems19, 2, 2007, 255-269.

• [31] Byeon J., Jeanjean L. and Tanaka K., Standing waves for nonlinear Schrödinger equations with a general nonlinearity : one and two dimensional cases, Comm. Part. Diff. Equa., 33, 4-6, 2008, 1113-1136.

• [32] Fukuizumi R. and Jeanjean L.,Stability of standing waves for a nonlinear Schrödinger equation with a repulsive Dirac delta potential, Discrete and Continuous Dynamical Systems (A),21, 1, 2008, 129-144.

• [33] Byeon J. and Jeanjean L., Erratum : Standing waves for nonlinear Schrödinger equations with a general nonlinearity, Archives for Rational Mechanics and Analysis, 190, 3, 2008, 549-551.

• [34] Cingolani S., Jeanjean L. and Secchi S.,Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions, ESAIM, COCV 15, 2009, 653-673.

• [35] Jeanjean L. and Le Coz S.,Instability for standing waves of nonlinear Klein-Gordon equations via mountain pass arguments, Transaction AMS 361, 2009, 5401-5416.

• [36] Byeon J., Jeanjean L. and Maris M.,Symmetry and monotonicity of least energy solutions, Calc. Var. Partial Differential Equations-36, 2009, 481-492.

• [37] Jeanjean L. and Squassina M., Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations, Ann. Inst. H. Poincaré, Anal. non-lin., 26, 2009, 1701-1716.

• [38] Colin M., Jeanjean L. and Squassina M., Stability and instability results for standing waves of quasilinear Schrödinger equations, Nonlinearity, 23, 2010, 1353-1385.

• [39] Jeanjean L. and Squassina M.,An approach to minimization under a constraint : The added mass technique, Calc. Var. Partial Differential Equations, 41, 2011, 511-534.

• [40] Jeanjean L., Some continuation properties via minimax arguments, Electron. J. Differential Equations, 48, 2011, 1-10.

• [41] Jeanjean L. and Sirakov B., Existence and multiplicity for elliptic problems with quadratic growth in the gradient, Comm. Part. Diff. Equa., 38, 2013, 244-264.

• [42] Bellazzini J., Jeanjean L. and Luo T., Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations, Proc. London Math.. Soc., 107, 2013, 303-339.

• [43] Jeanjean L. and Luo T., Sharp non-existence results of Prescribed L^2 norm solutions for some class of Schrödinger-Poisson and quasilinear equations, Zeitschrift fur Angewandte Mathematik und Physik, 64, 2013, 937-954.

• [44] Arcoya D., De Coster, C., Jeanjean L. and Tanaka K., Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions, J. Math. Anal. Appl., 420, 1, 2014, 772-780.

• [45] Arcoya D., De Coster, C., Jeanjean L. and Tanaka K., Continuum of solutions for an elliptic problem with critical growth in the gradient, J. Funct. Anal, 268, 8, 2015, 2298-2335.

• [46] Cingolani S., Jeanjean L. and Tanaka K., Multiplicity of positive solutions of nonlinear Schrödinger équations concentrating at a potential well, Calc. Var. Partial Differential Equations, 53, 1-2, 2015, 413-439.

• [47] Jeanjean L., Luo T. and Wang Z-Q., Multiple normalized solutions for quasi-linear Schrödinger equations, Journal of Differential Equations, 259, 8, 2015, 3894-3928.

• [48] Jeanjean L., Ramos Quoirin H., Multiple solutions for an indefinite problem with critical growth in the gradient, Proc. AMS, 144, 2, 2016, 575-586.

• [49] Bellazzini J., Jeanjean, L., On dipolar quantum gases in the unstable regime, SIAM J. Math. Anal., 48, 3, 2016, 2028-2058.

• [50] Bartsch T., Jeanjean, L. and Soave N., Normalized solutions for a system of coupled cubic Schrödinger equations on R^3, J. Math. Pures Appl., 106, 4, 2016, 583-614.

• [51] Gou T., Jeanjean, L., Existence and orbital stability of standing waves for nonlinear Schrödinger systems, Nonlinear Analysis, 144, 2016, 10-22.

• [52] De Coster C., Jeanjean, L., Multiplicity results in the non-coercive case for an elliptic problem with critical growth in the gradient, J. Differential Equations, 262, 2017, 5231-5270.

• [53] Cingolani S., Jeanjean, L. and Tanaka K., Multiple complex-valued solutions for nonlinear magnetic Schrödinger equations, Journal of Fixed Point Theory and Applications, 19,1, 2017, 37–66.

• [54] Bellazzini J., Boussaid N., Jeanjean, L., Visciglia N., Existence and stability of standing waves for supercritical NLS with a partial confinement, Communications in Mathematical Physics, 353, 1, 2017, 229-251.

• [55] Bartsch T., Jeanjean, L., Normalized solutions for nonlinear Schrödinger systems, Proc. Royal Soc. Edinburgh, A, 148, 2, 2018, 225-242.

• [56] Gou T., Jeanjean, L., Multiple positive normalized solutions for nonlinear Schrödinger systems, Nonlinearity, 31, 5, 2018, 2319-2345.

• [57] Bonheure D., Casteras J-B., Gou T., Jeanjean L., Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime, Trans. Amer. Math. Soc., 372, 3, 2019, 2167-2212.

• [58] Cingolani S., Jeanjean L., Stationary waves with prescribed L^2-norm for the planar Schrödinger-Poisson system, SIAM J. Math. Anal., 51, 4, 2019, 3533-3568.

• [59] Bonheure D., Casteras J-B., Gou T., Jeanjean L., Strong instability of ground states to a fourth order Schrödinger equation, International Mathematics Research Notices, 17, 2019, 5299-5315.

• [60] Jeanjean L., Lu S-S., Nonradial normalized solutions for nonlinear scalar field equations, Nonlinearity, 32, 12, 2019, 4942-4966.

• [61] De Coster C., Fernandez A. J., Jeanjean, L., A Priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient, J. Math. Pures Appl., 132, 2019, 308-333.

• [62] Jeanjean, L., Lu S-S., Nonlinear scalar field equations with general nonlinearity, Nonlinear Analysis, 190, 2020,111604.

• [63] Boussaid, N., Fernandez A. J., Jeanjean, Some remarks on a minimization problem associated to a fourth order nonlinear Schrödinger equation, arXiv:1910.13177

• [64] Jeanjean L., Lu S-S., A mass supercritical problem revisited, Calc. Var. Partial Differential Equations, 59, article number : 174, 2020.

• [65] Jeanjean L., Le, T. T., Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation, J. Differential Equations, 303, 2021, 277-325.

• [66] Dolbeault J., Frank R. L., Jeanjean L., Logarithmic estimates for mean-field models in dimension two and the Schrödinger-Poisson system, Comptes Rendus - Mathématique, 359(10), 2021, 1279-1293.

• [67] Jeanjean L., Lu S-S., On global minimizers for a mass constrained problem, Calc. Var. Partial Differential Equations, 61, (2022), no. 6, Paper No. 214.

• [68] Jeanjean L., Radulescu V., Nonhomogeneous quasilinear elliptic problems : linear and sublinear cases, J. Anal. Math. 146, 2022, 327-350.

• [69] Jeanjean L., Jendrej J., Le, T. T., Visciglia N., Orbital stability of ground states for a Sobolev critical Schrödinger equation, J. Math. Pures. Appl. 164, 2022, 158-179.

• [70] Fernandez A. J., Jeanjean L., Mandel R., Maris M., Non-homogeneous Gagliardo-Nirenberg inequalities in R^N and application to a biharmonic non-linear Schrödinger equation, J. Differential Equations, 328, 2022, 1-65.

• [71] Jeanjean L., Lu S-S., Normalized solutions with positive energies for a coercive problem and application to the cubic-quintic nonlinear Schrödinger equation, Math. Models Methods Appl. Sci. 32, 2022, no. 8, 1557-1588.

• [72] Jeanjean L., Le, T. T., Multiple normalized solutions for a Sobolev critical Schrödinger equation, Math. Ann., 384, 2022, no. 1-2, 101-134.

• [73] Borthwick J., Chang X., Jeanjean L., Soave N., Normalized solutions of L^2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities, Nonlinearity, 36, 2023, 3776-3795.

• [74] Chang X., Jeanjean L., Soave N., Normalized solutions of L^2-supercritical NLS equations on compact metric graphs, Ann. Inst. H. Poincaré (C) An. Non Lin., (2023). https://doi.org/10.4171/AIHPC/88.

• [75] Jeanjean L., Zhang J., Zhong X. A global branch approach to normalized solutions for the Schrödinger equation,J. Math. Pures. Appl. 183, 2024, 44-75.

• [76] Borthwick J., Chang X., Jeanjean L., Soave N., Bounded Palais-Smale sequences with Morse type information for some constrained functionals, to appear in Trans. Amer. Math. Soc.

• [77] Jeanjean L., Zhang J., Zhong X. Normalized ground states for a coupled Schrödinger system : mass super-critical case, arXiv:2311.10994.