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On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in R^N
nonlinear eigenvalue problem nonlinear Schr¨odinger equation orbital stability
2011/2/28
We study an eigenvalue problem for functions in RN and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability o...
EXISTENCE AND MULTIPLICITY RESULTS FOR A DEGENERATE ELLIPTIC EQUATIONS
degenerate elliptic equation mountain pass theorem maximal positive solution
2007/12/12
The goal of this paper is to study the multiplicity result of positive solutions of a class of degenerate elliptic equations. On the basis of the mountain pass theorems and the sub- and supersolutions...
Global Existence of Solutions for the Cauahy Problem of the Kawahara Equation with $L^2$ Initial Data
Kawahara equation Cauchy problem global solution
2007/12/11
In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Kawahara equation Cauchy problem global solution almost conservation law
2007/12/11
We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...