Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions

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...

Positive Solutions for p-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions

By employing upper and lower solutions method together with maximal principle, we establish a necessary and sufficient condition for the existence of pseudo-C3 0, 1 as well as C2 0, 1 positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t 0, t 1, and u 0. The dual results for the other integral b...

Positive solutions for higher - order nonlinear fractional differential equation with integral boundary condition ∗

In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo’s fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.

Existence and Uniqueness of Positive Solutions to Higher-order Nonlinear Fractional Differential Equation with Integral Boundary Conditions

In this article, we consider the nonlinear fractional order threepoint boundary-value problem D 0+u(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = u′(0) = · · · = u(n−2)(0) = 0, u(n−2)(1) = Z η