Triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities

In this paper, we study the existence of triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities. We first study the associated Green's function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. The results of this paper are new and extent previously known results

Existence and uniqueness of positive solutions to three-point boundary value problems for second order impulsive differential equations

Using a fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to three-point boundary value problems for second order impulsive differential equations

Positive solutions of second-order three-point boundary value problems with sign-changing coefficients

In this article, we investigate the boundary-value problem \begin{equation*} \begin{cases}x''(t)+h(t)f(x(t))=0,\quad t\in[0,1],\\ x(0)=\beta x'(0),\quad x(1)=x(\eta),\end{cases} \end{equation*} where $\beta\ge0$, $\eta\in(0,1)$, $f\in C([0,\infty), [0,\infty))$ is nondecreasing, and importantly $h$ changes sign on $[0,1]$. By the Guo-Krasnosel'skii fixed-point theorem in a cone, the existence of positive solutions is obtained via a special cone in terms of superlinear or sublinear behavior of $f$

Nonlinear triple-point problems with change of sign

WOS: 000253660200009In this paper, we study the existence of at least one or two positive solutions to the second-order triple-point nonlinear boundary value problem y"(x) + h(x) F(y(x)) = 0. x epsilon [a,b] y(a) = alpha y(eta), y(b) = beta y9 eta) where 0 < alpha < beta < 1 and eta epsilon (a, b). Here h changes sign in eta. As an application, we also give some examples to demonstrate Our results. (c) 2007 Elsevier Ltd. All rights reserved