Abstract
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.
Citation
Donal O'Regan. Nikolaos S. Papageorgiou. George Smyrlis. "Neumann problems with double resonance." Topol. Methods Nonlinear Anal. 39 (1) 151 - 173, 2012.
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