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Editorials' note

Miroslav Fiedler, Pankaj Jain, Lars-Erik Persson (2009)

Czechoslovak Mathematical Journal

Eigenvalues of the $p$ -Laplacian in $𝐑^{N}$ with indefinite weight

Yin Xi Huang (1995)

Commentationes Mathematicae Universitatis Carolinae

We consider the nonlinear eigenvalue problem $- {div (| \nabla u |}^{p - 2} {\nabla u) = λ g (x) | u |}^{p - 2} u$ in $𝐑^{N}$ with $p > 1$ . A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in $W^{1, p} (𝐑^{N})$ . A nonexistence result is also given for the case $p \geq N$ .

Elliptic resonance problems with unequal limits at infinity.

Martin Schechter (1994)

Mathematische Annalen

Energy and Morse index of solutions of Yamabe type problems on thin annuli

Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)

Journal of the European Mathematical Society

We consider the Yamabe type family of problems $(P_{ε}) : - Δ u_{ε} = u_{ε}^{(n + 2) / (n - 2)}$ , $u_{ε} > 0$ in $A_{ε}$ , $u_{ε} = 0$ on $\partial A_{ε}$ , where $A_{ε}$ is an annulus-shaped domain of $ℝ^{n}$ , $n \geq 3$ , which becomes thinner as $ε \to 0$ . We show that for every solution $u_{ε}$ , the energy $\int_{A_{ε}} | \nabla u_{|}^{2}$ as well as the Morse index tend to infinity as $ε \to 0$ . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on $ℝ^{n}$ , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...

Equivalence and zero sets of certain maps in infinite dimensions

Michal Fečkan (1993)

Commentationes Mathematicae Universitatis Carolinae

Equivalence and zero sets of certain maps on infinite dimensional spaces are studied using an approach similar to the deformation lemma from the singularity theory.

Errata-Corrigé : «Remarques sur les équations de Navier-Stokes stationnaires»

C. Foias, J. C. Saut (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Erratum to : “Multiple critical points of perturbed symmetric strongly indefinite functionals”

Denis Bonheure, Miguel Ramos (2009)

Annales de l'I.H.P. Analyse non linéaire

Esistenza e molteplicità di soluzioni per equazioni ellittiche nonlineari

Monica Musso (1998)

Bollettino dell'Unione Matematica Italiana

Euler-Poincaré index theory on Banach manifolds

A. J. Tromba (1975)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Existence and asymptotic behavior of solutions for weighted $p (t)$ -Laplacian system multipoint boundary value problems in half line.

Qiu, Zhimei, Zhang, Qihu, Wang, Yan (2009)

Journal of Inequalities and Applications [electronic only]

Existence and concentration of solutions for a $p$ -Laplace equation with potentials in $ℝ^{N}$ .

Wu, Mingzhu, Yang, Zuodong (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and multiplicity of nontrivial solutions for double resonance semilinear elliptic problems.

El Amrouss, Abdel R. (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations.

Mihăilescu, Mihai (2006)

Boundary Value Problems [electronic only]

Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

Nikolaos Papageorgiou, Francesca Papalini (2000)

Annales Polonici Mathematici

We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.

Currently displaying 1 – 20 of 37