The existence of positive solution of elliptic system by a linking theorem on product space.

DOI10.1016/J.NA.2003.09.010zbMath1100.35034OpenAlexW2005531762MaRDI QIDQ1427919

Xiying Wang, Pei-Hao Zhao

Publication date: 14 March 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2003.09.010

zbMATH Keywords

variational methodNehari manifoldnonlinear elliptic systemlinking theoremnontrivial positive solution

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60)

Related Items (11)

Multiple positive solutions for a critical quasilinear elliptic system ⋮ Existence results for some nonlinear elliptic systems ⋮ Nontrivial solutions for a quasilinear elliptic system ⋮ A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems ⋮ Existence of three nontrivial solutions for elliptic systems with critical exponents and weights ⋮ The existence of solutions for a class of semilinear elliptic systems ⋮ Multiple positive solutions for a critical elliptic system with concave and convex nonlinearities ⋮ Estimate of Morse index of cooperative elliptic systems and its application to spatial vector solitons ⋮ Multiple positive solutions for semi‐linear elliptic systems involving sign‐changing weight ⋮ Ground states for fractional nonlocal equations with logarithmic nonlinearity ⋮ Existence of infinitely many high energy solutions for a class of fractional Schrödinger systems

Cites Work

• A variational approach to subquadratic perturbations of elliptic systems
• Multiple positive solutions for some nonlinear elliptic systems
• Nonvariational elliptic systems
• Some remarks on a system of quasilinear elliptic equations
• Nehari's problem and competing species systems.
• Minimax theorems
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems
• Existence and Uniquenss of Positive Solutions for Certain Quasilinear Elliptic Systems
• Competing species systems with diffusion and large interactions
• On the Existence of Positive Solutions of Semilinear Elliptic Equations
• Uniqueness of solutions of nonlinear Dirichlet problems
• The existence of three nontrivial solutions of a class of elliptic systems

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