Electron. J. Differential Equations, Vol. 2020 (2020), No. 98, pp. 1-29.

Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities

Reshmi Biswas, Sweta Tiwari

Abstract:
In this article, using Nehari manifold method we study the multiplicity of solutions of the nonlocal elliptic system involving variable exponents and concave-convex nonlinearities,

where $\Omega\subset\mathbb R^N$, $N\geq2$ is a smooth bounded domain, $\lambda,\mu>0$ are parameters, and $s\in(0,1)$. We show that there exists $\Lambda>0$ such that for all $\lambda+\mu<\Lambda$, this system admits at least two non-trivial and non-negative solutions under some assumptions on $q,\alpha,\beta,a,b,c$.

Submitted November 2, 2019. Published September 23, 2020.
Math Subject Classifications: 35J48, 35J50, 35R11.
Key Words: Nonlocal problem with variable exponents; elliptic system; Nehari manifold; fibering map; concave-convex nonlinearities.

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Reshmi Biswas
Department of Mathematics
IIT Guwahati, Assam 781039, India
email: b.reshmi@iitg.ac.in
Sweta Tiwari
Department of Mathematics
IIT Guwahati, Assam 781039, India
email: swetatiwari@iitg.ac.in

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