NONLOCAL PROBLEM WITH INTEGRAL CONDITION FOR A FOURTH ORDER EQUATION

Approximate solution of fourth order differential equation in Neumann problem

Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution ...

A Nonlinear Second Order Problem Witha Nonlocal Boundary Condition

We study a nonlinear problem of pendulum-type for a p-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin’s continuation theorem for nonlinear operators, we prove the existence of a solution under a LandesmanLazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum eq...

Symmetric Positive Solutions for Nonlinear Singular Fourth-Order Eigenvalue Problems with Nonlocal Boundary Condition

We investigate nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition u 4 t − λh t f t, u, u′′ 0, 0 < t < 1, u 0 u 1 ∫0a s u s ds, u′′ 0 u′′ 1 ∫1 0b s u ′′ s ds, where a, b ∈ L1 0, 1 , λ > 0, h may be singular at t 0 and/or 1. Moreover f t, x, y may also have singularity at x 0 and/or y 0. By using fixed point theory in cones, an explicit interval for λ is derived ...

Initial-boundary Value Problem with a Nonlocal Condition for a Viscosity Equation

On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation