Nonresonance conditions on the potential for a second-order periodic boundary value problem

Second-Order Boundary Value Problem with Integral Boundary Conditions

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

On a Periodic Boundary Value Problem for Second-order Linear Functional Differential Equations

where ω > 0, : C([0,ω]) → L([0,ω]) is a linear bounded operator and q ∈ L([0,ω]). By a solution of the problem (1.1), (1.2) we understand a function u ∈ C̃′([0,ω]), which satisfies (1.1) almost everywhere on [0,ω] and satisfies the conditions (1.2). The periodic boundary value problem for functional differential equations has been studied by many authors (see, for instance, [1, 2, 3, 4, 5, 6, 8,...

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.