Mr. Ruijun Yang Profile

Ruijun Yang

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Proceedings Article | 28 July 2023 Paper

Multiple solutions for Kirchhoff type problem

Na Xu, Ruijun Yang

Proceedings Volume 12756, 1275644 (2023) https://doi.org/10.1117/12.2685896

KEYWORDS: Picosecond phenomena, Chromium, Wave equations, Vibration, Sodium, Elasticity

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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.

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