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

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


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