A multiplicity result for some Kirchhoff-type equations involving exponential growth condition in $\mathbb{R}^2 $

Sami  Aouaoui

doi:10.3934/cpaa.2016.15.1351

Article Contents

2016, Volume 15, Issue 4: 1351-1370. Doi: 10.3934/cpaa.2016.15.1351

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A multiplicity result for some Kirchhoff-type equations involving exponential growth condition in $\mathbb{R}^2 $

Sami Aouaoui^1,

1.
Institut Supérieur des Mathématiques Appliquées et de l'Informatique de Kairouan, Avenue Assad Iben Fourat, 3100 Kairouan

Received: October 31, 2015

Revised: December 31, 2015

Published: June 2016

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Abstract

In this paper, we consider the existence and multiplicity of sign-changing solutions to some Kirchhoff-type equation involving a nonlinear term with exponential growth. In a first result, we prove the existence of at least three solutions: one solution is positive, one is negative and the third one is sign-changing. The existence of infinitely many sign-changing solutions is proved as our second result in this work. Our method is mainly based on invariant sets of descending flow in the framework of classical critical point theory.

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Mathematics Subject Classification: Primary: 35J20, 35J62; Secondary: 35A15, 35B08, 35D30.

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