TY  - JOUR
AU  - Zahed, Hanadi 
PY  - 2020
TI  - Positive Solutions for Some Weighted Elliptic Problems
JF  - Journal of Mathematics and Statistics
VL  - 16
IS  - 1
DO  - 10.3844/jmssp.2020.125.132
UR  - https://thescipub.com/abstract/jmssp.2020.125.132
AB  - In this study, we study the existence and the nonexistence of positive solutions for the following nonlinear elliptic problems: 	(P)where, Ω is a regular bounded domain in ℝ , N ≥ 2, a(x) is a smooth function on   and f(x, s) is asymptotically linear in s at infinity, that is  = ℓ < ∞. We will prove that the problem (P) has a positive solution for ℓ large enough and does not have positive solutions for ℓ less than the first eigenvalue of the operator. We prove also that the method works for the case when f(x, s) is sub-critical and super-linear at +∞.2010 Mathematics Subject classification: 35J05, 35J65, 35J20, 35J60, 35K57, 35J70.