Infinite solutions having a prescribed number of nodes for a p-Laplacian problem

2014/11/28 by Jing Zeng, Zeng, Jing
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1411.7909

openalex publication_date 2014/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concern with the multiplicity of solutions for a p-Laplacian problem. A weaker super-quadratic assumptions is required on the nonlinearity. Under the weaker condition we give a new proof for the infinite solutions having a prescribed number of nodes to the problem. It turns out that the weaker condition on nonlinearity suffices to guarantee the infinitely many solutions. At the same time, a global characterization of the critical values of the nodal radial solutions are given.

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