Results 41 to 50 of about 690 (102)

The generalized Conley index and multiple solutions of semilinear elliptic problems

Abstract and Applied Analysis, Volume 1, Issue 1, Page 103-135, 1996., 1996
We establish some framework so that the generalized Conley index can be easily used to study the multiple solution problem of semilinear elliptic boundary value problems. Both the parabolic flow and the gradient flow are used. Some examples are given to compare our approach here with other well‐known methods.
E. N. Dancer, Yihong Du
wiley   +1 more source

Anisotropic problems with unbalanced growth

Advances in Nonlinear Analysis, 2020
The main purpose of this paper is to study a general class of (p, q)-type eigenvalues problems with lack of compactness. The reaction is a convex-concave nonlinearity described by power-type terms.
Alsaedi Ahmed, Ahmad Bashir
doaj   +1 more source

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

, 2012
We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 ...
______, ______, ______, ______, A. Ambrosetti, A. Ambrosetti, A. Azzollini, C. A. Stuart, C. D. Sogge, D. M. A. Stuart, E. Deumens, E. Long, F. A. Berezin, G. Vaira, H. Berestycki, I. Ianni, J. Shatah, J. Shatah, L. Aloui, L. Jeanjean, M. Beals, M. Grillakis, M. I. Weinstein, M. I. Weinstein, M. Keel, M. Ohta, Marco Ghimenti, Marco Squassina, R. K. Dodd, S. Cuccagna, S. Le Coz, S. Le Coz, Stefan Le Coz, T. Cazenave, T. Cazenave, T. D'Aprile, T. Tao, T.-C. Lin, V. Benci, Y. Liu, Y. Yu, Y.-G. Oh   +41 more
core   +3 more sources

On a theorem of H. Hopf

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 813-816, 1990., 1990
A simple proof of a theorem of H. Hopf [1], via Morse theory, is given.
Takis Sakkalis
wiley   +1 more source

On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent [PDF]

, 2006
We consider the nonlinear eigenvalue problem $-{\rm div}(|\nabla u|^{p(x)-2}\nabla u)=\lambda |u|^{q(x)-2}u$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded open set in $\RR^N$ with smooth boundary and $p$, $q$ are continuous ...
Mihailescu, Mihai, Radulescu, Vicentiu
core   +1 more source

Multiple perturbations of a singular eigenvalue problem

, 2015
We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle
Cencelj, Matija, Repovš, Dušan, Virk, Žiga   +2 more
core   +1 more source

The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations

, 2001
Abstract and Applied Analysis, Volume 6, Issue 2, Page 71-99, 2001.
E. N. Dancer, Kee Y. Lam, Shusen Yan
wiley   +1 more source

The β-Flatness Condition in CR Spheres

Advanced Nonlinear Studies, 2017
This work is an adaptation of one of the methods based on the variational critical points at infinity theory of Abbas Bahri [1, 3, 2, 4, 5, 6, 7, 8] to the Cauchy–Riemann settings.
Gamara Najoua, Hafassa Boutheina
doaj   +1 more source

Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Advances in Nonlinear Analysis, 2020
In this paper, we study the singularly perturbed fractional Choquard ...
Yang Zhipeng, Zhao Fukun
doaj   +1 more source

Critical fractional $p$-Laplacian problems with possibly vanishing potentials

, 2015
We obtain nontrivial solutions of a critical fractional $p$-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev ...
Perera, Kanishka, Squassina, Marco, Yang, Yang   +2 more
core   +1 more source