Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

Abstract

In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.2000 Mathematics Subject Classification. 34B15, 34B18.

Solvability for a nonlinear third-order three-point boundary value problem

“…In this way we remove the half of the assumptions to prove the existence of a solution when using Krasnoselskii's fixed point theorem. (See [10,17,19]). Moreover, we establish our results for t in [0, T ].…”

“…Since f ∞ = 0 and from Theorem 3.2, we can get that the (4.1)-(4.2) has at least one positive solution. Consequently, we cannot apply the Krasnoselskii's fixed point theorem like in [10,17,19] Example 4.2. Consider the boundary value problem where α = 15, η = 0, 2 = 1 5 , T = 3 4 , 0 < α = 15 < 37, 5 = 2T…”

“…On the other hand, we have f 0 = 1 , then the function f is not superlinear. Consequently, we cannot apply the Krasnoselskii's fixed point theorem like in [10,17,19]…”

Existence Results for a Nonlinear Fourth Order Ordinary Differential Equation with Four-Point Boundary Value Conditions

“…Boundary value problems (for short BVPs) for fourth order ordinary dierential equations (for short ODEs) are used to describe a huge number of physical, biological and chemical phenomena, see for instance [1,11,13,22,23,27] and references therein. In the last few decades, positive solution of two-point, three-point and four-point boundary value problems for second order, third order, fourth order as well as higher order has extensively been studied by using various techniques, see for instance [2,3,4,5,8,9,10,14,15,19,24,25,28] and references therein. Inspiring by the above-mentioned works, we have interested to check the existence of positive solutions of a four-point BVP for NLFOODE by applying upper and lower solution method [10] and Schauderâs xed point theorem [20].…”

Positive solutions of nonlinear third-order boundary value problem with integral boundary conditions

“…In 2016, Benaicha and Haddouchi. [1] studied the existence of positive solutions of a nonlinear two-point boundary value problem (BVP) for the following fourth-order differential equation…”