Abstract
<abstract><p>This paper is devoted to deriving several multiplicity results of nontrivial weak solutions to Kirchhoff-Schrödinger equations involving the $ p(\cdot) $-Laplace-type operator. The aims of this paper are stated as follows. First, under some conditions on a nonlinear term, we show that our problem has a sequence of infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the problem on a new class of nonlinear term. The primary tools to obtain such multiplicity results are the fountain theorem and the dual fountain theorem, respectively.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference50 articles.
1. C. O. Alves, S. B. Liu, On superlinear $p(x)$-Laplacian equations in $\mathbb R^{N}$, Nonlinear Anal., 73 (2010), 2566–2579. https://doi.org/10.1016/j.na.2010.06.033
2. S. N. Antontsev, S. Shmarev, Evolution PDEs with nonstandard growth conditions, Atlantis Press, Amsterdam, 2015. https://doi.org/10.2991/978-94-6239-112-3
3. D. Arcoya, J. Carmona, P. J. Martínez-Aparicio, Multiplicity of solutions for an elliptic Kirchhoff equation, Milan J. Math., 90 (2022), 679–689. https://doi.org/10.1007/s00032-022-00365-y
4. M. Avci, B. Cekic, R. A. Mashiyev, Existence and multiplicity of the solutions of the $p(x)$-Kirchhoff type equation via genus theory, Math. Method. Appl. Sci., 34 (2011), 1751–1759. https://doi.org/10.1002/mma.1485
5. J. Cen, S. J. Kim, Y. H. Kim, S. Zeng, Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent, Adv. Differential Equ., 2013, In press.
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献