Positive solutions for Kirchhoff problems with vanishing nonlocal term

João R. Santos Júnior; Gaetano Siciliano

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arXiv · 1709.06463

Positive solutions for Kirchhoff problems with vanishing nonlocal term

João R. Santos Júnior·Gaetano Siciliano

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Abstract

In this paper we study the Kirchhoff problem \begin{equation*} \left \{ \begin{array}{ll} -m(\| u \|^{2})\Delta u = f(u) & \mbox{in $\Omega$,} u=0 & \mbox{on $\partial\Omega$,} \end{array}\right. \end{equation*} in a bounded domain, allowing the function $m$ to vanish in many different points. Under an appropriated {\sl area condition}, by using a priori estimates, truncation techniques and variational methods, we prove a multiplicity result of positive solutions which are ordered in the $H_{0}^{1}(\Omega)$-norm.

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João R. Santos Júnior, Gaetano Siciliano. 2017-09-19. Positive solutions for Kirchhoff problems with vanishing nonlocal term. https://arxiv.org/abs/1709.06463

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