In this paper, we establish the existence of infinitely many solutions to a Neumann problem involving the p-Laplacian and with discontinuous nonlinearities. The technical approach is mainly based on a very recent result on critical points for possibly non-smooth functionals in a Banach space due to Marano and Motreanu, namely Theorem 1.1 in a paper that is to appear in the journal J. Diff. Eqns (see Theorem 2.3 in the body of this paper). Some applications are presented.
Candito, P. (2002). INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 45(2), 397-409 [10.1017/s0013091501000189].
INFINITELY MANY SOLUTIONS TO THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN AND WITH DISCONTINUOUS NONLINEARITIES
Candito, Pasquale
2002-01-01
Abstract
In this paper, we establish the existence of infinitely many solutions to a Neumann problem involving the p-Laplacian and with discontinuous nonlinearities. The technical approach is mainly based on a very recent result on critical points for possibly non-smooth functionals in a Banach space due to Marano and Motreanu, namely Theorem 1.1 in a paper that is to appear in the journal J. Diff. Eqns (see Theorem 2.3 in the body of this paper). Some applications are presented.
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