Existence and multiplicity of nontrivial solutions for semilinear elliptic Dirichlet problems across resonance

Xianojun Chang, Yong Li

Abstract


With the linear growth of the nonlinearity and a new compactness condition
involving the asymptotic behavior of its potential at infinity, we
establish the existence and multiplicity results of nontrivial
solutions for semilinear elliptic Dirichlet problems. The
nonlinearity may cross multiple eigenvalues.

Keywords


Semilinear elliptic problems; compactness condition; across resonance; Mountain pass theorem; Leray-Schauder degree

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