Electron. J. Differential Equations, Vol. 2017 (2017), No. 291, pp. 1-9.

Existence and non-existence of solutions for a singular problem with variable potentials

Kamel Saoudi

Abstract:
The purpose of this article is to prove some existence and nonexistence theorems for the inhomogeneous singular Dirichlet problem
$$ - \Delta_p u = \frac{\lambda k(x)}{u^\delta}\pm h(x) u^q. $$
For proving our results we use the sub and super solution method, and monotonicity arguments.

Submitted March 14, 2017. Published November 21, 2017.
Math Subject Classifications: 35J35, 35R05.
Key Words: Singular elliptic equation; variational methods; existence; non-existence.

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Kamel Saoudi
College of sciences at Dammam
University of Imam Abdulrahman Bin Faisal
31441 Dammam, Saudi Arabia
email: kasaoudi@gmail.com

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