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The scalar-curvature problem on the standard three-dimensional sphere
Let (S3, c) be the standard 3-sphere, i.e., the 3-sphere equipped with the standard metric. Let K be a C2 positive function on S3. The Kazdan-Warner problem [l] is the problem of finding suitableExpand
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On a variational problem with lack of compactness: the topological effect of the critical points at infinity
RésuméNous étudions les problèmes sous-critiquesPɛ:−Δu=up−ɛ,u > 0 surΩ;u=0 sur ∂Ω−oùΩ est un domaine borné et régulier de ℝN,N−3,p + 1=2N/N −2 est l'exposant critique de Sobolev, et ɛ>0 tend versExpand
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On the existence of a positive solution of semilinear elliptic equations in unbounded domains
We prove here the existence of a positive solution, under general conditions, for semilinear elliptic equations in unbounded domains with a variational structure. The solutions we build cannot beExpand
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A perturbation method in critical point theory and applications
This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s. Here, s c R^ is smooth and bounded, and h eExpand
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Morse index of some min-max critical points
On donne un resultat general sur des bornes inferieures pour des indices de Morse de points critiques obtenus par des principes de min-max. En combinant cette information avec une inegaliteExpand
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Solutions of superlinear elliptic equations and their morse indices
We consider here solutions of semilinear second-order elliptic equations with superlinear nonlinearities. And we present some relationships between their Morse Indices and some qualitativeExpand
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A minimax method for a class of Hamiltonian systems with singular potentials
Abstract This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. TheExpand
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Topological results on a certain class of functionals and application
We study in this paper problems of the type Δu + ¦u¦p − 1 u = ƒ(x), Ω bounded ⊂ RN, u = 0¦∂Ω, (I) where ƒ(x) is given and where p ϵ (1, (N + 2N − 2)) (p ϵ (1, + ∞) if N ⩽ 2). Our main result is thatExpand
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