Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

Ruichang Pei and Jihui Zhang

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

Abstract: We consider a class of particular Kirchhoff type problems with a right‐hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N = 2, 3). Namely, it is 4‐linear at −∞ and 4‐superlinear at +∞. However, it need not satisfy the Ambrosetti‐Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser‐Trudinger inequality.

Date: 2014
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https://doi.org/10.1155/2014/163645

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:163645

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