Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3

Ling Ding, Lin Li and Jin-Ling Zhang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3 |∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity. Under appropriate assumptions on k, f, and h, existence of two positive solutions is proved by using the Ekeland′s variational principle and the Mountain Pass Theorem in critical point theory.

Date: 2014
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https://doi.org/10.1155/2014/710949

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:710949

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