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.
Existence and multiplicity of solutions for a nonlinear Neumann problem / Vannella, Giuseppina. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 180:4(2002), pp. 429-440. [10.1007/s102310100020]
Existence and multiplicity of solutions for a nonlinear Neumann problem
Vannella, Giuseppina
2002-01-01
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.File in questo prodotto:
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