The study of higher-order resonant and non-resonant boundary value problems

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Singular Discrete Higher Order Boundary Value Problems

We study singular discrete nth order boundary value problems with mixed boundary conditions. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. AMS subject classification: 39A10, 34B16.

Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

and Applied Analysis 3 (C6) (P + JQN)γ(∂Ω 2 ) ⊂ C, (C7) Ψ γ (Ω 2 \ Ω 1 ) ⊂ C, then the equation Lx = Nx has a solution in the set C ∩ (Ω 2 \ Ω 1 ). 3. Positive Solution for the Nonresonant Problem In this section, we suppose that f ∈ C([0, 1] × [0, +∞), [0, +∞)) and ∑m−2 i=1 β i < 1. We begin with some preliminary results. Consider the problem x 󸀠󸀠󸀠 (t) + y (t) = 0, t ∈ [0, 1] , (10) x 󸀠󸀠 (0) =...

Boundary value problems for higher order parabolicequationsRussell

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...