Neumann problems with double resonance
Słowa kluczowe
Double resonance, C-condition, unique continuation property, critical groups, Morse theory, homotopy invarianceAbstrakt
We study elliptic Neumann problems in which the reaction term at infinity is resonant with respect to any pair $\{ \widehat{\lambda}_m, \widehat{\lambda}_{m+1}\}$ of distinct consecutive eigenvalues. Using variational methods combined with Morse theoretic techniques, we show that when the double resonance occurs in a ``nonprincipal'' spectral interval $[\widehat{\lambda}_m, \widehat{\lambda}_{m+1}]$, $ m\geq 1$, we have at least three nontrivial smooth solutions, two of which have constant sign. If the double resonance occurs in the ``principal'' spectral $[\widehat{\lambda}_0=0,\widehat{\lambda}_1]$, then we show that the problem has at least one nontrivial smooth solution.Pobrania
Opublikowane
2012-04-23
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1.
O’REGAN, Donal, PAPAGEORGIOU, Nikolaos S. & SMYRLIS, George. Neumann problems with double resonance. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 39, nr 1, s. 151–173. [udostępniono 22.7.2024].
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