On complex-valued solutions to a 2D eikonal equation

Giorgio Talenti

Displaying similar documents to “On complex-valued solutions to a 2D eikonal equation”

Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane (2014)

Open Mathematics

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In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Some critical point theorems and applications to semilinear elliptic partial differential equations

Paul H. Rabinowitz (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Some existence results for the scalar curvature problem via Morse theory

Andrea Malchiodi (1999)

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

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We prove existence of positive solutions for the equation $- △_{g_{0}} u + u = (1 + ϵ K (x)) u^{2^{*} - 1}$ on $S^{n}$ , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on $S^{n}$ , $2^{*}$ is the critical Sobolev exponent, and $ϵ$ is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.