On the Solution of An Ill-Posed Boundary Value Problem for Second-Order Evolution Equations

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

Boundary value problem for second-order impulsive functional differential equations

This paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. An example is discussed to illustrate the efficiency of the obtained result. © 2005 Elsevier Inc. All rights reserved.

An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains

The paper is concerned with properties of an ill-posed problem for the Helmholtz equation when Dirichlet and Neumann conditions are given only on a part Γ of the boundary ∂Ω. We present an equivalent formulation of this problem in terms of a moment problem defined on the part of the boundary where no boundary conditions are imposed. Using a weak definition of the normal derivative, we prove the...

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

On an Asymptotic Boundary Value Problem for Second Order Differential Equations

The existence of at least one solution to a nonlinear second order differential equation in Rk on the semi-infinite with the first derivative vanishing at infinity is proved by using topological methods. The second boundary condition is x(0) = 0 or x′(0) = 0.