We consider a symmetric semilinear boundary value problem having infinitely many solutions. We prove that, if we perturb this problem in a non-symmetric way, then the number of solutions goes to infinity as the perturbation tends to zero. The growth conditions on the nonlinearities do not ensure the smoothness of the associated functional.
Degiovanni, M., Radulescu, V., Perturbations of nonsmooth symmetric nonlinear eigenvalue problems, <<COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE>>, 1999; 329 (4): 281-286. [doi:10.1016/S0764-4442(00)88567-5] [https://hdl.handle.net/10807/312925]
Perturbations of nonsmooth symmetric nonlinear eigenvalue problems
Degiovanni, Marco
Primo
Conceptualization
;
1999
Abstract
We consider a symmetric semilinear boundary value problem having infinitely many solutions. We prove that, if we perturb this problem in a non-symmetric way, then the number of solutions goes to infinity as the perturbation tends to zero. The growth conditions on the nonlinearities do not ensure the smoothness of the associated functional.
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