The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

the nehari manifold for a class of indefinite weight semilinear elliptic equations

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...

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 *   ...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

Existence Results for a Class of Semilinear Degenerate Elliptic Equations

We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.

Compact Embeddings and Indefinite Semilinear Elliptic Problems

Our purpose is to find positive solutions u ∈ D(R ) of the semilinear elliptic problem −∆u = h(x)u for 2 < p. The function h may have an indefinite sign. Key ingredients are a h-dependent concentration-compactness Lemma and a characterization of compact embeddings of D(R ) into weighted Lebesgue spaces.