An initial boundary value problem for a partial differential equation of higher even order with a Bessel operator

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

an analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

On Initial Boundary Value Problem with Dirichlet Integral Conditions for a Hyperbolic Equation with the Bessel Operator

We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formu...

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation