Multiple solutions for Kirchhoff type problem

Na Xu; Ruijun Yang

doi:10.1117/12.2685896

28 July 2023 Multiple solutions for Kirchhoff type problem

Na Xu, Ruijun Yang

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275644 (2023) https://doi.org/10.1117/12.2685896
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

We consider the problem −( a+b∫_R^N|∇w|²dy)▵w + H(y)w = g(y,w), y∈R^N where a,b > 0 and H( y) ∈ C (R^N,R) is a sign-changing function. With a subquadratic growth g , the existence of multiple solutions of the Kirchhoff equation is proved. The (PS) condition is proved. And, we prove the functional J satisfies the local linking geometry and J is bounded from below. The problem has two nontrivial solutions by using the local linking theorem.

Citation Download Citation

Na Xu and Ruijun Yang "Multiple solutions for Kirchhoff type problem", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275644 (28 July 2023); https://doi.org/10.1117/12.2685896

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