A second-order nonlinear boundary value problem

Nonlinear second-order multivalued boundary value problems

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

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.

Existence of Positive Solutions of a Nonlinear Second-order Boundary-value Problem with Integral Boundary Conditions

In this article we prove the existence of at least one positive solution for a three-point integral boundary-value problem for a second-order nonlinear differential equation. The existence result is obtained by using Schauder’s fixed point theorem. Therefore, we do not need local assumptions such as superlinearity or sublinearity of the involved nonlinear functions.

A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

and Applied Analysis 3 In BVP 1.4 – 1.6 , it can be found that the boundary condition 1.5 is dependent on all the x a , x b , x′ a , and x′ b terms. First, existence and uniqueness of solutions of BVP 1.4 – 1.6 is established by combining the method of upper and lower solutions with LeraySchauder degree theory. Then, the general quasilinearization method is applied to construct the approximatio...

Second-Order Boundary Value Problem with Integral Boundary Conditions