Multiplicity result for asymptotically linear noncooperative elliptic systems

2012 ◽  
Vol 36 (12) ◽  
pp. 1533-1542
Author(s):  
Guanggang Liu ◽  
Shaoyun Shi ◽  
Yucheng Wei
Keyword(s):  
Elliptic Systems ◽  
Multiplicity Result ◽  
Asymptotically Linear

scholarly journals ASYMPTOTICALLY LINEAR ELLIPTIC SYSTEMS WITH PARAMETERS

2010 ◽  
Vol 52 (2) ◽  
pp. 383-389 ◽  
Author(s):  
CHAOQUAN PENG
Keyword(s):  
Bounded Domain ◽  
Trivial Solution ◽  
Elliptic Systems ◽  
Continuous Functions ◽  
Asymptotically Linear ◽  
Smooth Bounded Domain ◽  
Negative Numbers ◽  
Solution Pair ◽  
Image Position

AbstractIn this paper, we show that the semi-linear elliptic systems of the form (0.1) possess at least one non-trivial solution pair (u, v) ∈ H01(Ω) × H01(Ω), where Ω is a smooth bounded domain in ℝN, λ and μ are non-negative numbers, f(x, t) and g(x, t) are continuous functions on Ω × ℝ and asymptotically linear at infinity.

A multiplicity result for asymptotically linear Kirchhoff equations

2017 ◽  
Vol 8 (1) ◽  
pp. 267-277 ◽  
Author(s):  
Chao Ji ◽  
Fei Fang ◽  
Binlin Zhang
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Type Equation ◽  
Ground State Solution ◽  
Mountain Pass ◽  
Multiplicity Result ◽  
Asymptotically Linear ◽  
Type Solution ◽  
Kirchhoff Equations ◽  
Kirchhoff Type

Abstract In this paper, we study the following Kirchhoff type equation: -\bigg{(}1+b\int_{\mathbb{R}^{N}}\lvert\nabla u|^{2}\,dx\biggr{)}\Delta u+u=a(% x)f(u)\quad\text{in }\mathbb{R}^{N},\qquad u\in H^{1}(\mathbb{R}^{N}), where {N\geq 3} , {b>0} and {f(s)} is asymptotically linear at infinity, that is, {f(s)\sim O(s)} as {s\rightarrow+\infty} . By using variational methods, we obtain the existence of a mountain pass type solution and a ground state solution under appropriate assumptions on {a(x)} .

Asymptotically Linear Elliptic Systems

2004 ◽  
Vol 29 (5-6) ◽  
pp. 925-954 ◽  
Author(s):  
Gongbao Li ◽  
Jianfu Yang
Keyword(s):  
Elliptic Systems ◽  
Asymptotically Linear

scholarly journals A multiplicity result for a class of strongly indefinite asymptotically linear second order systems

2010 ◽  
Vol 72 (6) ◽  
pp. 2874-2890 ◽  
Author(s):  
Anna Capietto ◽  
Francesca Dalbono ◽  
Alessandro Portaluri
Keyword(s):  
Second Order ◽  
Multiplicity Result ◽  
Asymptotically Linear ◽  
Second Order Systems

scholarly journals POSITIVE SOLUTIONS FOR ASYMPTOTICALLY LINEAR ELLIPTIC SYSTEMS

2007 ◽  
Vol 49 (2) ◽  
pp. 377-390 ◽  
Author(s):  
CHAOQUAN PENG ◽  
JIANFU YANG
Keyword(s):  
Positive Solution ◽  
Bounded Domain ◽  
Elliptic Systems ◽  
Continuous Functions ◽  
Asymptotically Linear ◽  
Smooth Bounded Domain ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Solution Pair ◽  
Image Position

AbstractIn this paper, we show that the semilinear elliptic systems of the form (0.1) possess at least one positive solution pair (u, v) ∈ H10(Ω) × H10(Ω), where Ω is a smooth bounded domain in $\mathbb{R}^N$, f(x,t) and g(x, t) are continuous functions on $\Omega\times \mathbb{R}$ and asymptotically linear at infinity.

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