Electron. J. Differential Equations, Vol. 2016 (2016), No. 295, pp. 1-12.

Perturbed subcritical Dirichlet problems with variable exponents

Ramzi Alsaedi

We study a class of nonhomogeneous elliptic problems with Dirichlet boundary condition and involving the p(x)-Laplace operator and power-type nonlinear terms with variable exponent. The main results of this articles establish sufficient conditions for the existence of nontrivial weak solutions, in relationship with the values of certain real parameters. The proofs combine the Ekeland variational principle, the mountain pass theorem and energy arguments.

Submitted September 8, 2016. Published November 16, 2016.
Math Subject Classifications: 35J60, 58E05.
Key Words: Nonhomogeneous elliptic problem; variable exponent; Dirichlet boundary condition; mountain pass theorem.

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Ramzi Alsaedi
Department of Mathematics
Faculty of Sciences, King Abdulaziz University
P.O. Box 80203, Jeddah 21589, Saudi Arabia
email: ramzialsaedi@yahoo.co.uk

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