A geometrical view of the Nehari manifold

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

Gluing Approximate Solutions of Minimum Type on the Nehari Manifold

In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems. This note is concerned with the procedure of gluing mountain-pass type solutions. The rst procedure to glue mountain-pass type solutions was developed through the work of S er e, and Coti Zelati-Rabinowitz. Th...

The Nehari Manifold for Fractional Systems Involving Critical Nonlinearities

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, μ) belongs to a suitable subset of R.

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

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 *   ...