On a boundary value problem for a high order mixed type equation

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

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.

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

Mixed Problem with Nonlocal Boundary Conditions for a Third-order Partial Differential Equation of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem. 2000 Mathematics Subject Classification. 35B45, 35K20, 35M10.

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