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Solutions of superlinear elliptic equations and their morse indices
Abbas Bahri,Pierre-Louis Lions +1 more
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In this paper, the authors consider solutions of semilinear second-order elliptic equations with superlinear nonlinearities and present some relationships between their Morse Indices and some qualitative properties.Abstract:
We consider here solutions of semilinear second-order elliptic equations with superlinear nonlinearities. And we present some relationships between their Morse Indices and some qualitative properties. In particular we show that for, “uo;subcritical” nonlinearities, bounds on solutions are equivalent to bounds on their Morse indices.read more
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
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On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
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On the classification of solutions of the Lane-Emden equation on unbounded domains of Rn
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Selected new aspects of the calculus of variations in the large
Ivar Ekeland,Nassif Ghoussoub +1 more
TL;DR: In this paper, the authors discuss some of the recent developments in variational methods while emphasizing new applications to nonlinear problems, including the formulation of variational set-ups which provide more information on the location of critical points and therefore on the qualitative properties of the solutions of corresponding Euler-Lagrange equations.
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Multiple Bound States of Nonlinear Schrödinger Systems
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TL;DR: In this article, the existence of bound states for Schrodinger systems has been studied in the context of mathematical physics, and different approaches have been proposed depending upon the sizes of the interaction parameters in the system.
References
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Journal ArticleDOI
Solutions of Hartree-Fock equations for Coulomb systems
TL;DR: In this paper, the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizacker equation is investigated.
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A perturbation method in critical point theory and applications
Abbas Bahri,Henri Berestycki +1 more
TL;DR: In this paper, the existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s.
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Multiple critical points of perturbed symmetric functionals
TL;DR: In this article, the effect of perturbations which are not small and which destroy the symmetry for two classes of such problems was studied and it was shown that multiple solutions persist despite the perturbation.
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Morse index of some min‐max critical points. I. Application to multiplicity results
A. Bahri,Pierre-Louis Lions +1 more
TL;DR: In this paper, a resultat general sur des bornes inferieures for des indices de Morse de points critiques obtenus par des principes de min-max is presented.