On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value
Articles
G. A. Afrouzi
Mazandaran University, Iran
S. H. Rasouli
Mazandaran University, Iran
Published 2006-11-01
https://doi.org/10.15388/NA.2006.11.4.14736
PDF

Keywords

positive solutions
sub-super solution

How to Cite

Afrouzi, G.A. and Rasouli, S.H. (2006) “On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value”, Nonlinear Analysis: Modelling and Control, 11(4), pp. 323–329. doi:10.15388/NA.2006.11.4.14736.
Crossref
6
Scopus
0
Crossref Logo
G A AFROUZI, J VAHIDI (2011)
On critical exponent for the existence and stability properties of positive weak solutions for some nonlinear elliptic systems involving the (p, q)-Laplacian and indefinite weight function. Proceedings - Mathematical Sciences, 121(1), 83.
Crossref Logo
R. Guefaifia, Т. Bouali, S. H. Rasouli (2025)
A new result on the existence of positive solutions for a class of fractional Kirchhoff-type systems with multiple parameters. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika(1), 15.
Crossref Logo
Imed Bachar, Habib Mâagli, Hassan Eltayeb (2023)
Existence and Uniqueness of Positive Solution for Some Semipositone Schrödinger Boundary Value Problems in Bounded Domains. Mediterranean Journal of Mathematics, 20(4).
Crossref Logo
Toufik Moussaoui, Radu Precup (2009)
Existence results for semilinear elliptic boundary value problems via topological methods. Applied Mathematics Letters, 22(1), 126.
Crossref Logo
A. Shabanpour, S.H. Rasouli (2025)
Analysis of positive solutions for classes of Laplacian systems with sign change weight functions and nonlinear boundary conditions. Results in Applied Mathematics, 25, 100525.
Crossref Logo
Rafik Guefaifia, S. H. Rasouli (2025)
Existence of positive weak solutions for a class of fractional Laplacian systems with sign-changing weight functions. Indian Journal of Pure and Applied Mathematics.

Abstract

This study concerns the existence of positive solutions to classes of boundary value problems of the form
−∆u = g(x,u), x ∈ Ω,
u(x) = 0, x ∈ ∂Ω,
where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

PDF

Downloads