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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...
Existence of Nonnegative Solutions to Singular Semi-positone Problems
semi-positone problem singularity green function
2007/12/11
In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown. ...
Global Existence of a Shock for the Supersonic Flow Past a Curved Wedge
potential equation shock wave wedge global existence
2007/12/11
This note is devoted to the study of the global existence of a shock wave for the super- sonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle...
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...
Existence Theorems for Periodic Differential Inclusions in I\!R$^{\hbox{$^N$}}$
Differential inclusion multifunction upper and lower semicontinuity extremal periodic solution Schauder fixed point theorem property $\ssize {\mathcal{U}}$ weak norm Hartman condition
2007/12/11
We study the periodic problem for differentialinclusions in $\ssize \Bbb{R}^N$. First we look for extremalperiodic solutions. Using techniques from multivalued analysis anda fixed point argument we es...
The Existence of Maximal $W^*$-Closed Submodules in Nest Algebra Modules
Finite-partition submodule Finite Finite rank operator $w^{*}$-closure
2007/12/11
Using the technique of annihilators, we characterize the $w^{*}$-closure of the finite-partition submodule ${{\mathscr R}({\mathscr N}, \sim)}$ of a weakly closed nest algebra module ${\mathscr U}$ co...
The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem
third-order ordinary differential equation
2007/12/11
The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed poin...
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})...
Stability and Existence of Multidimensional Subsonic Phase Transitions
multidimensional subsonic phase transitions
2007/12/10
The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to estab...
On the Existence of Positive Periodic Solutions for Neutral Functional Differential Equation with Multiple Deviating Arguments
positive periodic solution k-set contraction
2007/12/10
By means of an abstract continuation theory for k-set contraction and continuation theorem of coincidence degree principle, some criteria are established for the existence of positive periodic solutio...
On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian
quasi-asymptotically linear weak solution critical point
2007/12/10
1): {-Δ_pu≡-div |▽u|~(p-2)▽u)=f(x,u), x∈Ω, u=0, x∈partial deriv Ω, where Ω is a bounded domain in R~N (N≥1) and f(x, u) is quasi-asymptotically linear with respect to |u|~(p-2) u at infinity. Recently...
The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator
Generalized polar coordinates Laplacian-like operator
2007/12/10
The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.
Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model
global existence positive periodic solution
2007/12/10
By using the continuation theorem of Mawhin's coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model {u...
GLOBAL EXISTENCE AND DECAY ESTIMATES FOR SOLUTIONS OF DEGENERATE PARABOLIC EQUATIONS
Parabolic equation existence
2007/12/10
In this paper, we will show the existence and certain decay estimate of the global solutions for the initial-boundary value problemin the smooth bounded domain Ω＝Rn. n≥2.
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...