‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.

We study the Nehari manifold for a class of quasilinear elliptic systems involving a pair of (p,q)-Laplacian operators and a parameter. We prove the existence of a nonnegative nonsemitrivial solution for the systems by discussing properties of the Nehari manifold, and so global bifurcation results are obtained. Thanks to Picone’s identity, we also prove a nonexistence result.

a class of kirchhoff type systems with nonlinear boundary conditions considered in this paper. by using the method of nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.

‎using nehari manifold methods and mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-kirchhoff-type system are established.

1 1 , , 0, , r s p u u h x u dx g x u dx x u x + + −∆ = + ∈ Ω = ∈ ∂Ω () 1, 0 p W Ω () () () 1 1 , 0. r s p u x h x u dx g x u dx in u on + +  −∆ = + Ω   = ∂Ω   () E () () 1 1 / r p s Np N p N p < < − < < − + − () () () 0 0 r h L L C ∞ ∈ Ω Ω Ω   0 1 1 1, r r p * + + = ()() 0. 1 Np r Np r N p = − + − () () 0 s g L L ∞ ∈ Ω Ω  0 1 1 1, s s p * + + = ()() 0 ,. 1 Np Np s p Np s N p N p *   ...

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...