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Displaying similar documents to “On nodal radial solutions of an elliptic problem involving critical Sobolev exponent”

A refinement of the radial Pohozaev identity

Florin Catrina (2010)

Mathematica Bohemica

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In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.

An elliptic equation with no monotonicity condition on the nonlinearity

Gregory S. Spradlin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle...

Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity

Antonio Ambrosetti, Veronica Felli, Andrea Malchiodi (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this preliminary Note we outline the results of the forthcoming paper [2] dealing with a class on nonlinear Schrödinger equations with potentials vanishing at infinity. Working in weighted Sobolev spaces, the existence of a ground state is proved. Furthermore, the behaviour of such a solution, as the Planck constant tends to zero (semiclassical limit), is studied proving that it concentrates at a point.