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arXiv · 1710.02120

Existence results of positive solutions for Kirchhoff type equations via bifurcation methods

Willian Cintra·João R. Santos Júnior·Gaetano Siciliano·Antonio Suárez
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Abstract

In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -\Delta(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~\Omega, u>0& \mbox{in}~\Omega, u= 0& \mbox{on}~\partial\Omega, \end{array} \right. \end{equation*} in a bounded and smooth domain $\Omega$ in ${\rm I}\hskip -0.85mm{\rm R}$. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters $a,b,p,r$ and the nonlinearity $g$, the existence of positive solutions.

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Willian Cintra, João R. Santos Júnior, Gaetano Siciliano, Antonio Suárez. 2017-10-05. Existence results of positive solutions for Kirchhoff type equations via bifurcation methods. https://arxiv.org/abs/1710.02120

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