Elliptic Weighted Problem with Indefinite Asymptotically Linear Nonlinearity
- 1 Taibah University, Saudi Arabia
The objective of this paper is the study the following nonlinear elliptic problem involving a weight function:
-div(a(x)∇υ) = f(x, u) in Ω and u = 0 on ∂Ω (P)
where, Ω is a regular bounded subset and ℝN ≥ 2, a(x) is a nonnegative function and f(x, t) is allowed to be sign-changing. We employ variational techniques to prove the existence of a nontrivial solution for the problem (P), under some suitable assumptions, when the nonlinearity is asymptotically linear. Then, we prove by the same method the existence of positive solution when the function f is superlinear and subcritical at infinity.
Copyright: © 2021 Hanadi Zahed and Laila A. Alnaser. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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- Elliptic Problem
- Asymptotically Linear
- Nonnegative Weight Function
- Indefinite Nonlinearity
- Variational Method