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Displaying 1 – 20 of 39

A complement to the Fredholm theory of elliptic systems on bounded domains.

Rabier, Patrick J. (2009)

Boundary Value Problems [electronic only]

A maximum principle for systems with variational structure and an application to standing waves

Nicholas D. Alikakos, Giorgio Fusco (2015)

Journal of the European Mathematical Society

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.

A predator-prey model with combined death and competition terms

Joon Hyuk Kang, Jungho Lee (2010)

Czechoslovak Mathematical Journal

The existence of a positive solution for the generalized predator-prey model for two species $\begin{matrix} Δ u + u (a + g (u, v)) = 0 in Ω, \\ Δ v + v (d + h (u, v)) = 0 in Ω, \\ u = v = 0 on \partial Ω, \end{matrix}$ are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.

Asymptotic behavior of ground state solution for Hénon type systems.

Wang, Ying, Yang, Jianfu (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of entire positive solutions for a class of semilinear elliptic systems.

Zhang, Zhijun (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of entire solutions for semilinear elliptic systems under the Keller-Osserman condition.

Zhang, Zhijun, Shi, Yongxiu, Xue, Yanxing (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.

Nguyen Thanh Chung (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of nonnegative solutions to positone-type problems in $ℝ^{N}$ with indefinite weights.

Rajendran, Dhanya, Tyagi, Jagmohan (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems.

Djellit, Ali, Moussaoui, Mohand, Tas, Saadia (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for a class of elliptic systems in $ℝ^{N}$ involving the $(p (x), q (x))$ -Laplacian.

Ogras, S., Mashiyev, R.A., Avci, M., Yucedag, Z. (2008)

Journal of Inequalities and Applications [electronic only]

Existence of solutions for a system of elliptic partial differential equations.

Dalmasso, Robert (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for elliptic systems with nonlocal terms in one dimension.

Cabada, Alberto, Cid, J.Ángel, Sanchez, Luís (2011)

Boundary Value Problems [electronic only]

Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.

Cardoulis, Laure (2001)

International Journal of Mathematics and Mathematical Sciences

Existence of weak solutions for a nonlinear elliptic system.

Fang, Ming, Gilbert, Robert P. (2009)

Boundary Value Problems [electronic only]

Existence result for a class of elliptic systems with indefinite weights in $ℝ^{2}$ .

Zhang, Guoqing, Liu, Sanyang (2008)

Boundary Value Problems [electronic only]

Existence result for a class of nonlinear elliptic systems on punctured unbounded domains.

Colin, Fabrice (2010)

Boundary Value Problems [electronic only]

Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth

Hui Zhang, Junxiang Xu, Fubao Zhang, Miao Du (2014)

Open Mathematics

For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle.

Infinitely many periodic solutions for variable exponent systems.

Guo, Xiaoli, Lu, Mingxin, Zhang, Qihu (2009)

Journal of Inequalities and Applications [electronic only]

Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems

Fukun Zhao, Leiga Zhao, Yanheng Ding (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the following periodic Hamiltonian elliptic system ${- Δ ϕ + V (x) ϕ = G_{ψ} (x, ϕ, ψ) in ℝ^{N}, - Δ ψ + V (x) ψ = G_{ϕ} (x, ϕ, ψ) in ℝ^{N}, ϕ (x) \to 0 and ψ (x) \to 0 as | x | \to \infty .$ Assuming the potential V is periodic and 0 lies in a gap of $σ (- Δ + V)$ , $G (x, η)$ is periodic in x and asymptotically quadratic in $η = (ϕ, ψ)$ , existence and multiplicity of solutions are obtained via variational approach. 

Infinitely many solutions of strongly indefinite semilinear elliptic systems.

Chen, Kuan-Ju (2009)

Boundary Value Problems [electronic only]

Currently displaying 1 – 20 of 39

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