The Initial Boundary Value Problems for a Class of Multidimensional Nonlinear Pseudo-Hyperbolic System of Higher Order

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

Sinc-Galerkin method for solving a class of nonlinear two-point boundary value problems

In this article, we develop the Sinc-Galerkin method based on double exponential transformation for solving a class of weakly singular nonlinear two-point boundary value problems with nonhomogeneous boundary conditions. Also several examples are solved to show the accuracy efficiency of the presented method. We compare the obtained numerical results with results of the other existing methods in...

On Some Boundary Value Problems for Nonlinear Degenerate Hyperbolic Equations of Higher Order

The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and...

Tariel Kiguradze ON SOLVABILITY AND WELL-POSEDNESS OF INITIAL–BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR HYPERBOLIC EQUATIONS

The sufficient conditions for unique local solvability, global solvability and of well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations are studied.

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...