Positive solution for the Kirchhoff-type equations involving general subcritical growth

Jiu  Liu; Jia-Feng  Liao; Chun-Lei Tang

doi:10.3934/cpaa.2016.15.445

Article Contents

2016, Volume 15, Issue 2: 445-455. Doi: 10.3934/cpaa.2016.15.445

This issue Previous Article Schrödinger-Kirchhoff-Poisson type systems Next Article Competing interactions and traveling wave solutions in lattice differential equations

Positive solution for the Kirchhoff-type equations involving general subcritical growth

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715
2.
School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received: March 2015

Revised: November 2015

Published: March 2016

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Abstract

In this paper, the existence of a positive solution for the Kirchhoff-type equations in $\mathbb{R}^N$ is proved by using cut-off and monotonicity tricks, which unify and sharply improve the results of Li et al. [Existence of a positive solution to Kirchhoff type problems without compactness conditions, J. Differential Equations 253 (2012) 2285--2294]. Our result cover the case where the nonlinearity satisfies asymptotically linear and superlinear at infinity.

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Mathematics Subject Classification: 35B09, 35B38, 35J20.

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References

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