Existence and multiplicity of solutions for a nonlinear Neumann problem |
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Authors: | Giuseppina Vannella |
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Institution: | (1) Dipartimento Interuniversitario di Matematica, Via Orabona 4, 70125 Bari, Italia, e-mail: vannella@dm.uniba.it, IT |
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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.
Received: October 30, 1999 Published online: December 19, 2001 |
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Keywords: | : PDE – critical points – Morse theory |
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