Existence of multiple solutions to elliptic equations satisfying a global eigenvalue-crossing condition
https://ejde.math.txstate.edu/Volumes/2013/145/duc.pdfPublisher, magazine: ,
Publication year: 2013
Lưu Trích dẫn Chia sẻAbstract
We study the multiplicity of solutions to the elliptic equation ∆u+ f(x, u) = 0, under the assumption that f(x, u)/u crosses globally but not pointwise any eigenvalue for every x in a part of the domain, when u varies from −∞ to ∞. Also we relax the conditions on uniform convergence of f(x, s)/s, which are essential in many results on multiplicity for asymptotically linear problems.
Tags: Index of critical points; mountain pass type; nonlinear elliptic equations; multiplicity of solutions.
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