Second-order Nonlocal Boundary Value Problems Research Articles

Non-local second-order boundary value problems with derivative-dependent nonlinearity.

We prove the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with nonlinear term having derivative dependence. We allow the nonlinearity to grow quadratically with respect to derivatives. We obtain a priori bounds for norms of derivatives by using a recently obtained Gronwall-type inequality. Three examples illustrate some of the results. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.

Solvability for second-order nonlocal boundary value problems with "Equation missing"

Abstract The existence of at least one solution to the second-order nonlocal boundary value problems on the real line is investigated by using an extension of Mawhin’s continuation theorem. MSC: 34B10, 34B40, 34B15.

Solvability for nonlocal boundary value problems on a half line with "Equation missing"

Abstract The existence of at least one solution to the second-order nonlocal boundary value problems on a half line is investigated by using Mawhin’s continuation theorem. MSC: 34B10, 34B40, 34B15.

Three symmetric positive solutions for second-order nonlocal boundary value problems

Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form \( \begin{gathered} u''\left( t \right) + g\left( t \right)f\left( {t,u\left( t \right)} \right) = 0, 0 < t < 1, \hfill \\ u\left( 0 \right) = u\left( 1 \right) = \int_0^1 {m\left( s \right)u} \left( s \right)ds, \hfill \\ \end{gathered} \) where m ∈ L1[0, 1], g: (0, 1) → [0,∞) is continuous, symmetric on (0, 1) and maybe singular at t = 0 and t = 1, f: [0, 1] × [0,∞) → [0,∞) is continuous and f(·, x) is symmetric on [0, 1] for all x ∈ [0,∞).

Exact solutions of a class of second-order nonlocal boundary value problems and applications

In this paper, solutions of a class of second-order differential equations with some multi-point boundary conditions are studied. We give exact expressions of the solutions for the linear m-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the positive solutions for a nonlinear singular second-order m-point boundary value problem.

Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line

This paper investigates the solvability of the second-order boundary value problems with the one-dimensional p-Laplacian at resonance on a half-line 8 < : (c(t)�p(x 0 (t))) 0 = f(t,x(t),x 0 (t)), 0 < t < 1, x(0) = n P i=1 µix(�i), lim t!+1 c(t)�p(x 0 (t)) = 0

Positive solutions to a system of second-order nonlocal boundary value problems

In this paper we study the existence of positive solutions to a system of second-order nonlocal boundary value problems by using fixed point index theory in a cone. Our hypotheses imposed on nonlinearities are those which characterize systems of nonlocal boundary value problems, and our boundary value conditions are expressed in terms of possibly nonlinear functions of Riemann–Stieltjes integrals, thus generalizing and unifying the boundary value conditions in the literature. Therefore our results cannot be routinely deduced from the ones for single nonlocal problem in the literature.