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Open AccessArticle
Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities
by
Yun-Ho Kim
Yun-Ho Kim
Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea
Fractal Fract. 2024, 8(7), 426; https://doi.org/10.3390/fractalfract8070426 (registering DOI)
Submission received: 11 June 2024
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Revised: 16 July 2024
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Accepted: 19 July 2024
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Published: 20 July 2024
Abstract
This paper is concerned with nonlocal fractional p-Laplacian Schrödinger–Hardy-type equations involving concave–convex nonlinearities. The first aim is to demonstrate the -bound for any possible weak solution to our problem. As far as we know, the global a priori bound for weak solutions to nonlinear elliptic problems involving a singular nonlinear term such as Hardy potentials has not been studied extensively. To overcome this, we utilize a truncated energy technique and the De Giorgi iteration method. As its application, we demonstrate that the problem above has at least two distinct nontrivial solutions by exploiting a variant of Ekeland’s variational principle and the classical mountain pass theorem as the key tools. Furthermore, we prove the existence of a sequence of infinitely many weak solutions that converges to zero in the -norm. To derive this result, we employ the modified functional method and the dual fountain theorem.
Share and Cite
MDPI and ACS Style
Kim, Y.-H.
Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities. Fractal Fract. 2024, 8, 426.
https://doi.org/10.3390/fractalfract8070426
AMA Style
Kim Y-H.
Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities. Fractal and Fractional. 2024; 8(7):426.
https://doi.org/10.3390/fractalfract8070426
Chicago/Turabian Style
Kim, Yun-Ho.
2024. "Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities" Fractal and Fractional 8, no. 7: 426.
https://doi.org/10.3390/fractalfract8070426
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