scholarly journals Non-existence of ground states for a semilinear elliptic system of Lane-Emden-Fowler type

2013 ◽  
Vol 29 (2) ◽  
pp. 187-193
Author(s):  
MIODRAG IOVANOV ◽  
Keyword(s):  
Elliptic System ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Aequationes Math ◽  
Radial Solutions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Positive Radial Solutions ◽  
Radially Symmetric Solutions

We obtain sufficient conditions for the non-existence of positive radially symmetric solutions for a class of Lane, Emden and Fowler elliptic systems. In our result, the nonlinear term it was suggested by the work of [D. O’Regan and H. Wang, Positive radial solutions for p-Laplacian systems, Aequationes Math., 75 (2008) 43–50].

Positive solutions for some competitive elliptic systems

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Ramzi Alsaedi ◽  
Habib Mâagli ◽  
Noureddine Zeddini
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Elliptic System ◽  
Elliptic Systems ◽  
Global Behavior ◽  
Continuous Solutions ◽  
Kato Class ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Compact Boundary

AbstractUsing some potential theory tools and the Schauder fixed point theorem, we prove the existence of positive bounded continuous solutions with a precise global behavior for the semilinear elliptic system Δu = p(x)u α ν r in domains D of ℝn, n ≥ 3, with compact boundary (bounded or unbounded) subject to some Dirichlet conditions, where α ≥ 1, β ≥ 1, r ≥ 0, s ≥ 0 and the potentials p, q are nonnegative and belong to the Kato class K(D).

Positive Radial Solutions for Elliptic Systems with Nonlocal Conditions

2012 ◽  
Vol 204-208 ◽  
pp. 4800-4808
Author(s):  
Sheng Li Xie
Keyword(s):  
Fixed Point ◽  
Elliptic System ◽  
Fixed Point Index ◽  
Nonlocal Conditions ◽  
Elliptic Systems ◽  
Index Theory ◽  
Point Index ◽  
Radial Solutions ◽  
Fixed Point Index Theory ◽  
Positive Radial Solutions

By using fixed point index theory,we study the existence of positive radial solutions and multiple positive radial solutions for the elliptic system with nonlocal conditions. Our results extend and improve some existing ones.

On a Class of Reversible Elliptic Systems

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Paul H. Rabinowitz
Keyword(s):  
Elliptic System ◽  
Existence Of Solutions ◽  
Elliptic Systems ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

AbstractFor a semilinear elliptic system of PDE’s which is spatially reversible, we establish the existence of solutions in C

scholarly journals Existence, Nonexistence and Multiplicity Results for Positive Radial Solutions of n−dimensional Elliptic System

2021 ◽  
pp. 35-45
Author(s):  
Yalin Shen
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Information Science ◽  
Elliptic Systems ◽  
Point Index ◽  
Radial Solutions ◽  
Multiplicity Results ◽  
Positive Radial Solutions ◽  
Multiplicity Of Positive Solutions

Aims/ Objectives: In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the n−dimensional elliptic system  systems have been widely studied, but there is relatively little research on n-dimensional elliptic systems. We are very interested in this subject and want to study it. We give new conclusions on the existence, nonexistence and multiplicity of positive solutions for the n-dimensional elliptic system. Study Design: Study on the existence, nonexistence and multiplicity of positive solutions. Place and Duration of Study: School of Applied Science, Beijing Information Science & Technology University, September 2019 to present. Methodology: We prove the existence, nonexistence and multiplicity of positive solutions by the results of fixed point index. Results: We give new conclusions of existence, nonexistence and multiplicity of positive solutionsfor the system. Conclusion: We prove the existence, nonexistence and multiplicity of positive solutions to the n-dimensional elliptic system   and give new conclusions.

scholarly journals Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yongju Yang ◽  
Xinguang Zhang
Keyword(s):  
Blow Up ◽  
Elliptic Systems ◽  
Entire Space ◽  
Bounded Solutions ◽  
Radial Solutions ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Blowing Up ◽  
Quadratic Gradient

We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms,Δui+|∇ui|2=pi(|x|)fi(u1,u2,…,ud)fori=1,2,…,donRN,N≥3andd∈{1,2,3,…}. We establish the conditions onpithat ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition onfiis simple and different to the Keller-Osserman condition.

Existence, uniqueness and stability of positive solutions to sublinear elliptic systems

2011 ◽  
Vol 141 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Jann-Long Chern ◽  
Yong-Li Tang ◽  
Chang-Shou Lin ◽  
Junping Shi
Keyword(s):  
Bifurcation Diagram ◽  
Elliptic System ◽  
Positive Solutions ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Hölder Continuous ◽  
Asymptotical Behaviour ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System

The existence, stability and uniqueness of positive solutions to a semilinear elliptic system with sublinear nonlinearities are proved. It is shown that the precise global bifurcation diagram of the positive solutions is a monotone curve with different asymptotical behaviour according to the form of the nonlinearities. Equations with Hölder continuous nonlinearities are also considered.

Sign in / Sign up

Export Citation Format

Share Document