Positive solutions of a fourth-order differential equation with integral boundary conditions

summary:We study the existence of positive solutions to the fourth-order two-point boundary value problem $$\begin {cases} u^{\prime \prime \prime \prime }(t) + f(t,u(t))=0, & 0 < t < 1,\\ u^{\prime }(0) = u^\prime (1) = u^{\prime \prime }(0) =0, & u(0) = \alpha [u], \end {cases}$$ where $\alpha [u]=\int ^{1}_{0}u(t){\rm d}A(t)$ is a Riemann-Stieltjes integral with $A \geq 0$ being a nondecreasing function of bounded variation and $f \in \mathcal {C}([0,1] \times \mathbb {R}_{+}, \mathbb {R}_{+})$. The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii's fixed point theorem and the Avery-Peterson fixed point theorem

Existence of Solutions by Coincidence Degree Theory for Hadamard Fractional Differential Equations at Resonance

Using the Coincidence Degree Theory of Mawhin and Constructing Appropriate Operators, We Investigate the Existence of Solutions to Hadamard Fractional Differential Equations (FRDEs) at Resonanc

Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem

summary:We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative

On oscillatory linear differential equations of third order

summary:Sufficient conditions are obtained in terms of coefficient functions such that a linear homogeneous third order differential equation is strongly oscillatory

Asymptotic behaviour of solutions of delay differential equations of nn-th order

summary:This paper deals with property A and B of a class of canonical linear homogeneous delay differential equations of $n$-th order

ftp ejde.math.txstate.edu (login: ftp) ON ASYMPTOTIC BEHAVIOUR OF OSCILLATORY SOLUTIONS FOR FOURTH ORDER DIFFERENTIAL EQUATIONS

Abstract. We establish sufficient conditions for the linear differential equations of fourth order (r(t)y ′′ ′ (t)) ′ = a(t)y(t) + b(t)y ′ (t) + c(t)y ′ ′ (t) + f(t) so that all oscillatory solutions of the equation satisfy lim y(t) = lim t→ ∞ t→ ∞ y ′ (t) = lim t→ ∞ y′ ′ (t) = lim t→ ∞ r(t)y′′ ′ (t) = 0, where r: [0, ∞) → (0, ∞), a, b, c and f: [0, ∞) → R are continuous functions. A suitable Green’s function and its estimates are used in this paper. 1