<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, we study the existence of positive solutions of the Dirichlet problem -Δu = λ p(x)f(u; v) ; -Δv = λ q(x)g(u; v); in D, and u = v = 0 on ∂∞D, where D ⊂ Rn (n ≥ 3) is an C1,1-domain with compact boundary and λ > 0. The potential functions p; q are not necessarily bounded, may change sign and the functions f; g : ℝ2 → ℝ are continuous with f(0; 0) > 0, g(0; 0) > 0. By applying the Leray- Schauder fixed point theorem, we establish the existence of positive solutions for λ sufficiently small. </abstract>

In this paper, we study the existence of positive solutions of the Dirichlet problem -Δu = λ p(x)f(u; v) ; -Δv = λ q(x)g(u; v); in D, and u = v = 0 on ∂∞D, where D ⊂ Rn (n ≥ 3) is an C1,1-domain with compact boundary and λ > 0. The potential functions p; q are not necessarily bounded, may change sign and the functions f; g : ℝ2 → ℝ are continuous with f(0; 0) > 0, g(0; 0) > 0. By applying the Leray- Schauder fixed point theorem, we establish the existence of positive solutions for λ sufficiently small.

Positive solutions for semilinear elliptic systems with sign-changing potentials

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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{"article-title":"Positive solutions for semilinear elliptic systems with sign-changing potentials"}

In this paper, we study the existence of positive solutions of the Dirichlet problem -Δu = λ p(x)f(u; v) ; -Δv = λ q(x)g(u; v); in D, and u = v = 0 on ∂∞D,...

Positive solutions for semilinear elliptic systems with sign-changing potentials

Published Online: Sep 21, 2017

Page range: 383 - 390

Received: Jan 24, 2014

Accepted: Mar 09, 2014

DOI: https://doi.org/10.1515/auom-2016-0023

Keywords
Elliptic Systems, Positive Solution, Green potential, Leray-Shauder fixed point theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Positive solutions for semilinear elliptic systems with sign-changing potentials

Published Online: Sep 21, 2017

Page range: 383 - 390

Received: Jan 24, 2014

Accepted: Mar 09, 2014

DOI: https://doi.org/10.1515/auom-2016-0023

KeywordsElliptic Systems, Positive Solution, Green potential, Leray-Shauder fixed point theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Elliptic Systems, Positive Solution, Green potential, Leray-Shauder fixed point theorem