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arXiv · 1708.03399

Multiplicity of solutions for resonant and non-resonant asymptotically linear elliptic problems

José R. S. Nascimento·Marcos T. O. Pimenta·João R. Santos Júnior
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Abstract

Results about existence of a signed ground state solution and multiple solutions (if $f$ is odd with respect to the second variable) are proven for a class of asymptotically linear elliptic problems involving a Carath\'eodory type nonlinearity satisfying assumptions weaker than (fF) in \cite{GLZ} or $(F_{2})_{+}$ in \cite{CM}. A close relation between the behaviour of $\lim_{|t|\to \infty}f(x, t)/|t|$ and the number of solutions is stablished.

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José R. S. Nascimento, Marcos T. O. Pimenta, João R. Santos Júnior. 2017-08-10. Multiplicity of solutions for resonant and non-resonant asymptotically linear elliptic problems. https://arxiv.org/abs/1708.03399

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