Twin n-point boundary value problems

Twin n-point boundary value problems

We establish the existence of positive solutions to twin time-scale problems given by the dynamic equation −u∆∇(t) = ηa(t)f(u(t)), t ∈ (t1, tn) ⊂ T with boundary conditions u(t1) = n−1 ∑ i=2 αiu(ti), u(tn) = 0, or u(t1) = 0, u(tn) = n−1 ∑ i=2 αiu(ti), using a functional-type cone expansion-compression fixed point theorem.

Positive solutions of $n$th-order $m$-point boundary value problems

‎In this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎As an application‎, ‎we give an example to demonstrate our main result.

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

B-SPLINE METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

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...