Investigating the existence and multiplicity of solutions to φ(x)-Kirchhoff problem

چکیده مقاله

In this article, we want to discuss variational methods such as the Mountain pass theorem and the Symmetric Mountain pass theorem, without the Ambrosetti-Rabinowitz condition. We prove the existence and multiplicity of nontrivial weak solutions for the problem of the following form [Formula Presented] where α ≥ β > 0, ∆_φ(x) υ is the φ(x)-Laplacian operator, Ω is a smooth bounded domain in R^N with smooth boundary ∂Ω and ν is the outer unit normal to [Formula Presented] with [Formula Presented] is a real parameter and[Formula Presented]. © 2024 A. Sadeghi et al.