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arxiv: 1710.10422 · v1 · pith:MXS6APS6new · submitted 2017-10-28 · 🧮 math.AP

Resonant semilinear Robin problems with a general potential

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keywords potentialproblemresonantrobinsemilinearcarathconsiderdriven
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We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term is a Carath\'eodory function which is resonant with respect to any nonprincipal eigenvalue both at $\pm \infty$ and 0. Using a variant of the reduction method, we show that the problem has at least two nontrivial smooth solutions.

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