Existence and multiplicity of solutions for fractional \(p_{1}(x,\cdot )\& p_{2}(x,\cdot )\)-Laplacian Schrödinger-type equations with Robin boundary conditions

IF 1.7 4区 数学 Q1 Mathematics Boundary Value Problems Pub Date : 2024-03-13 DOI:10.1186/s13661-024-01844-4
Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li
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Abstract

In this paper, we study fractional $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in $\mathbb{R}^{N}\setminus \overline{\Omega}$ for fractional order $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results.
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带罗宾边界条件的分数(p_{1}(x,\cdot )& p_{2}(x,\cdot ))-拉普拉奇薛定谔型方程的解的存在性和多重性
本文研究了罗宾边界条件下的分数 $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -拉普拉斯薛定谔型方程。在一些合适的假设条件下,我们利用山口稃和埃克兰德变分原理证明了两个解的存在。然后,分别运用喷泉定理和 Krasnoselskii 属理论推导出了无穷多个解的存在性。与之前的结果不同,本文的主题是分数阶 $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian 薛定谔型方程(包括凹凸非线性)的 $\mathbb{R}^{N}\setminus \overline\{Omega}$ 中的 Robin 边界条件。此外,我们还举了两个例子来说明我们的结果。
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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