JournalsaihpcVol. 31, No. 1pp. 155–167

Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior

  • Fuyi Li

    School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China

  • Junping Shi

    School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China; Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA

  • Zhanping Liang

    School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China
Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior cover
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Abstract

Existence and bifurcation of positive solutions to a Kirchhoff type equation

are considered by using topological degree argument and variational method. Here is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff type equation in bounded domain, and in our results the nonlinearity may be resonant near zero or infinity.

Cite this article

Fuyi Li, Junping Shi, Zhanping Liang, Positive solutions to Kirchhoff type equations with nonlinearity having prescribed asymptotic behavior. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 1, pp. 155–167

DOI 10.1016/J.ANIHPC.2013.01.006