Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems

The Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type

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 *   ...

MULTIPLICITY RESULTS FOR p-SUBLINEAR p-LAPLACIAN PROBLEMS INVOLVING INDEFINITE EIGENVALUE PROBLEMS VIA MORSE THEORY

We establish some multiplicity results for a class of p-sublinear pLaplacian problems involving indefinite eigenvalue problems using Morse theory.

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Existence and Multiplicity of Solutions for Semipositone Problems Involving p-Laplacian

The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system ðEk;lÞ involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters ðk;lÞ belongs to a certain subset of R. 20...