Mahmoud El Ahmadi, Mohamed Bouabdallah, A. Lamaizi
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引用次数: 0
摘要
本研究的重点是研究涉及分数 p(x)-Laplacian 算子的基尔霍夫问题。目的是研究在函数 f 和 m 的适当假设条件下,上述问题弱解的存在性和多重性。通过使用带有 Cerami 条件的山口定理,我们证明了在不假设 Ambrosetti-Rabinowitz 条件的情况下,该问题存在非三值弱解。此外,我们的第二个目的是确定λ 的精确正区间,对于该区间,上述问题至少有两个非难弱解。需要注意的是,无穷多个弱解的存在是通过福泉定理来证明的。
Existence and multiplicity results for Kirchhoff-type superlinear problems involving the fractional p(x)-Laplacian satisfying (C)-condition
Our focus in this study revolves around investigating a Kirchhoff problem involving the fractional p(x)-Laplacian operator. The purpose is to study the existence and multiplicity of weak solutions for the above problem under appropriate hypotheses on functions f and m. By using the Mountain Pass Theorem with Cerami condition, we show the existence of non-trivial weak solution for the problem without assuming the Ambrosetti-Rabinowitz condition. Furthermore, our second purpose is to determine the precise positive interval of λ for which the above problem admits at least two nontrivial weak solutions. It should be noted that the existence of infinitely many weak solutions is proved by employing the Fountain Theorem.