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A Class of Special Solutions for the Ultradiscrete Painleve II Equation
ultradiscretization Painleve equation Airy equation q-difference equation
2011/10/9
Abstract: A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending...
New Exact Solutions of a Generalized Shallow Water Wave Equation
Exact Solutions Generalized Shallow Water Wave Equation
2010/4/2
In this work an extended Jacobian elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave s...
Solutions for 2nth order lidstone BVP on time scales
Lidstone boundary value problem upper and lower solutions fixed point theorem positive solution
2010/2/25
In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive sol...
On completeness of elementary generalized solutions of a class of operator-differential equations of a higher order
Hilbert space existence of generalized solution operator-differential equation
2010/2/25
In this paper we give definition of m-fold completeness and prove a theorem on completeness of elementary generalized solution of corresponding boundary value problems at which the equation describes ...
The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian
p-Laplacian Avery-Peterson fixed-point theorem positive solution boundary value problem
2010/2/25
This paper deals with the multiplicity results of positive solutions of one-dimensional singular p-Laplace equation (jp(u'(t)))'+a(t)f(t,u(t),u'(t))=0, 0subject to the nonlinear boundary conditio...
Regularity of Solutions of the Cahn-Hilliard Equation with non-Constant Mobility
Cahn--Hilliard equation regularity Schauder estimates
2007/12/12
In this paper, we study the regularity of solutions for two-dimensional Cahn--Hilliard equation with non-constant mobility. Basing on the $L^p$ type estimates and Schauder type estimates, we prove the...
Positive and Nontrivial Solutions for the Urysohn Integral Equation
Urysohn integral equation positive solutions eigenvalues
2007/12/12
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficien...
Existence of Periodic Solutions for Second Order Rayleigh Equations With Piecewise Constant Argument
Rayleigh equation deviating argument piecewise constant argument periodic solution Mawhin's continuation theorem
2010/2/26
Based on a continuation theorem of Mawhin, periodic solutions are found for the second-order Rayleigh equation with piecewise constant argument.
On Positive Solutions of Boundary Value Problems for Nonlinear Second Order Difference Equations
Difference equations boundary value problems positive solutions Green's function fixed point theorem in cones
2010/2/26
In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence r...