Abstract
The aim of this paper is to investigate the existence of weak solutions for a boundary value problem of a second order differential equation. As the main tool, we apply a Krasnosel’skii type fixed point theorem in conjunction with the technique of measures of weak noncompactness in Banach spaces. Finally, two examples are given to illustrate our abstract results.
Highlights
1 Introduction In this paper, we investigate the existence of weak solutions for the boundary value problem of second order differential equations of the form x(t) – g(t, x(t))
Boundary value problems arise in a variety of applied mathematics and physics areas
Small size bridges are often designed with two supported points, which leads to a two-point boundary value problem: u (t) + υ(t) + φ t, u(t) = 0, 0 < t < 1, u(0) = 0, u(1) = 0
Summary
We investigate the existence of weak solutions for the boundary value problem of second order differential equations of the form x(t) – g(t, x(t)). Boundary value problems arise in a variety of applied mathematics and physics areas (refer to [1, 2] etc.). Some boundary value problems of ordinary equations may be turned into (1.1)-(1.2). Small size bridges are often designed with two supported points, which leads to a two-point boundary value problem (cf [3]):. If we define x(t) = g(t, x(t)) + h(t, x(t))u(t) for the known functions g and h, and f (t, x(t)) = υ(t) + φ(t, u(t)), the above problem is turned into (1.1)-(1.2)
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