Homogenization of oblique boundary value problems

On the Oblique Boundary Value Problems for Monge-ampère Equations

(1.3) β(x) · ν(x) > 0, φu(x, u) ≤ −γ0(x) < 0. Here ν is the unit outer normal to ∂Ω, γ0 is a positive function on ∂Ω, and Dβ = β · ∇. The existence and uniqueness of the classical convex solution of the equations (1.1) and (1.2) under some suitiable conditions on f, φ and ν was studied by P.L. Lions, N. Trudinger and J. Urbas [9]. They applied the method of continuity plus a priori estimates to...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...