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Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
Nonlinear Evolution Equations Locally Monotone Operators
2010/11/9
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical resu...
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
the blowup/global existence dichotomy the focusing cubic nonlinear Klein-Gordon equation
2010/11/15
We present some numerical findings concerning the nature of the blowup vs. global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation in three dimensions for radial data. The co...
On the existence of bounded solutions for a nonlinear elliptic system
bounded solutions a nonlinear elliptic system
2010/11/9
This work deals with the system $(-\Delta)^m u= a(x)\, v^p$, $(-\Delta)^m v=b(x)\, u^q$ with Dirichlet boundary condition in a domain $\Omega\subset\RR^n$, where $\Omega$ is a ball if $n\ge 3$ or a sm...
On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
Nonlinear Schr¨odinger equation Global existence Blow up in Nonlinear Schr¨odinger equation Global existence
2010/11/29
In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem−iut = u − V (x)u + f(x, |u|2)u + (W ⋆ |u|2)u, x ∈ RN, t > 0,u(x, 0) = u0(x), x ...
EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS
Nontrivial solution biharmonic equation
2007/12/17
4) is the critical sobolev exponent. This result is a extension of [1].
Global Existence of Small Solutions for Cubic Quasi-linear Klein-Gordon Systems in one Space Dimension
Cubic Quasi-linear Klein--Gordon systems One space dimension Global existence Asym-ptotic behavior
2007/12/12
In this paper, we consider a system of two cubic quasi-linear Klein--Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such...
EXISTENCE OF POSITIVE SOLUTIONS TO FOURTH ORDER QUASILINEAR BOUNDARY VALUE PROBLEMS
fourth-order boundary value problem fixed point theorem positive solution
2007/12/11
In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some f...
Global Existence and Nonexistence for a Strongly Coupled Parabolic System with Nonlinear Boundary Conditions
Strongly coupled Global existence Finite time blow-up Upper and lower solutions
2007/12/10
This paper deals with the strongly coupled parabolic system $u_{t}=v^{m}{\Delta}u,v_{t}=u^{n}{\Delta}v,\ (x,t)$ $\in {\Omega}\times (0,T)$ subject to nonlinear boundary conditions ${\partial}u/{\parti...
By using the perturbation theories on sums of ranges ofnonlinear accretive mappings of Calvert and Gupta, we study theabstract results on the existence of a solution $u \inL^{s}({\it\Omega})$ of nonli...
EXISTENCE OF MULTIPLE SOLUTIONS AND BIFURCATION FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS
Biharmonic equation critical exponent mu
2007/8/7
We inverstigate in this paper the existence problem for a critical semilinear biharmonic problem defined on a bounded domain.It is verified that the Palais-Smale condition holds true in certain interv...
AN EXISTENCE THEOREM FOR RADIAL POSITIVE SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS
Existence radial solution degenerate e
2007/8/7
We study the existence of positive solutions of nonlinear degenerate elliptic equations with the aid of phase-energy method. The equivalent conditions are given for the existence of positive solutions...