Abstract.
We consider a Neumann problem of the type -εΔu+F ′(u(x))=0 in an open bounded subset Ω of R n, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
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Received: October 30, 1999 Published online: December 19, 2001
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Vannella, G. Existence and multiplicity of solutions for a nonlinear Neumann problem. Ann. Mat. Pura Appl. IV. Ser. 180, 429–440 (2002). https://doi.org/10.1007/s102310100020
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DOI: https://doi.org/10.1007/s102310100020