Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions

DOI10.1016/j.amc.2014.01.073zbMath1410.34019OpenAlexW1966091942MaRDI QIDQ1646114

Mei Jia, Xi-Ping Liu

Publication date: 22 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.01.073

zbMATH Keywords

upper and lower solutionsmultiplicity of solutionsfractional differential equationsLeray-Schauder degree theoryintegral boundary value problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Fractional ordinary differential equations (34A08)

Related Items (60)

Solvability for Multi-Point BVP of Nonlinear Fractional Differential Equations at Resonance with Three Dimensional Kernels ⋮ The positive solutions for integral boundary value problem of fractional \(p\)-Laplacian equation with mixed derivatives ⋮ Infinitely many solutions for impulsive fractional boundary value problem with \(p\)-Laplacian ⋮ Positive solutions for integral boundary value problem of two-term fractional differential equations ⋮ Nontrivial solutions of a class of fractional differential equations with \(p\)-Laplacian via variational methods ⋮ Existence and nonexistence of positive solutions for fractional integral boundary value problem with two disturbance parameters ⋮ Nonlocal problems of fractional systems involving left and right fractional derivatives at resonance ⋮ Extremal solutions for some periodic fractional differential equations ⋮ A class of impulsive vibration equation with fractional derivatives ⋮ Extremal solutions for singular fractional \(p\)-Laplacian differential equations with nonlinear boundary conditions ⋮ Positive solution of a system of integral equations with applications to boundary value problems of differential equations ⋮ Existence of positive solutions for integral boundary value problems of fractional differential equations with \(p\)-Laplacian ⋮ Iterative technique for coupled integral boundary value problem of non-integer order differential equations ⋮ Existence of positive solutions for fractional differential equation with integral boundary conditions on the half-line ⋮ The positive solutions of infinite-point boundary value problem of fractional differential equations on the infinite interval ⋮ Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods ⋮ Solutions of fractional differential equations with \(p\)-Laplacian operator in Banach spaces ⋮ Multiple positive solutions for perturbed nonlinear fractional differential system with two control parameters ⋮ Infinitely many solutions for fractional differential system via variational method ⋮ Upper and lower solutions method for higher order fractional initial value problems ⋮ The method of lower and upper solutions for mixed fractional four-point boundary value problem with \(p\)-Laplacian operator ⋮ The method of upper and lower solutions for a class of fractional differential coupled systems ⋮ Multiplicity results for impulsive fractional differential equations with \(p\)-Laplacian via variational methods ⋮ Multiple solutions for a class of \(p\)-Laplacian type fractional boundary value problems with instantaneous and non-instantaneous impulses ⋮ Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions ⋮ A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems ⋮ The multiplicity of solutions for a class of nonlinear fractional Dirichlet boundary value problems with \(p\)-Laplacian type via variational approach ⋮ Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions ⋮ Existence results for convection‐reaction fractional problem involving the distributional Riesz derivative ⋮ Multiple solutions for nonlocal fractional Kirchhoff type problems ⋮ On the existence of solution to a boundary value problem of fractional differential equation on the infinite interval ⋮ Solvability of fractional multi-point boundary value problems with nonlinear growth at resonance ⋮ Existence of solutions for fractional multi-point boundary value problems at resonance with three-dimensional kernels ⋮ The method of lower and upper solutions for the general boundary value problems of fractional differential equations with \(p\)-Laplacian ⋮ Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity ⋮ Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval ⋮ Existence and uniqueness of the solutions for fractional differential equations with nonlinear boundary conditions ⋮ Positive solution for singular fractional differential equations involving derivatives ⋮ Twin solutions to semipositone boundary value problems for fractional differential equations with coupled integral boundary conditions ⋮ Nontrivial solutions for impulsive fractional differential equations via Morse theory ⋮ Fractional Sobolev space with Riemann-Liouville fractional derivative and application to a fractional concave-convex problem ⋮ ON POSITIVE SOLUTIONS OF EIGENVALUE PROBLEMS FOR A CLASS OF <i>P</i>-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATIONS ⋮ EXISTENCE OF SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATION WITH <i>P</i>-LAPLACIAN THROUGH VARIATIONAL METHOD ⋮ The monotone iterative method for the integral boundary value problems of fractional \(p\)-Laplacian equations with delay ⋮ Variational methods to the \(p\)-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem ⋮ Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions ⋮ Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives ⋮ Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations ⋮ Multiple positive solutions for four-point boundary value problem of fractional delay differential equations with \(p\)-Laplacian operator ⋮ The existence and nonexistence of positive solutions for fractional differential equations with nonhomogeneous boundary conditions ⋮ Nontrivial solutions for a class of perturbed fractional differential systems with impulsive effects ⋮ Monotone and concave positive solutions to three-point boundary value problems of higher-order fractional differential equations ⋮ Solvability of some fractional boundary value problems with a convection term ⋮ The convergence and stability analysis of the Jacobi collocation method for solving nonlinear fractional differential equations with integral boundary conditions ⋮ Multiple positive solutions for nonlinear fractional differential equations with integral boundary value conditions and a parameter ⋮ Positive solutions of fractional \(p\)-Laplacian equations with integral boundary value and two parameters ⋮ Positivity for integral boundary value problems of fractional differential equations with two nonlinear terms ⋮ SOLVABILITY FOR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEMS OF BAGLEY-TORVIK EQUATIONS AT RESONANCE ⋮ The positive solutions of fractional differential equation with Riemann-Stieltjes integral boundary conditions ⋮ A class of nonlocal problems of fractional differential equations with composition of derivative and parameters

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotone iterative sequences for nonlinear boundary value problems of fractional order
• On the solution of the fractional nonlinear Schrödinger equation
• Monotone iterative method for the second-order three-point boundary value problem with upper and lower solutions in the reversed order
• The existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions in reverse order
• Three nonnegative solutions for fractional differential equations with integral boundary conditions
• Solvability of fractional three-point boundary value problems with nonlinear growth
• Fractional order adaptive high-gain controllers for a class of linear systems
• Subordination and superordination for univalent solutions for fractional differential equations
• Multiple solutions for fractional differential equations with nonlinear boundary conditions
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Boundary value problems involving upper and lower solutions in reverse order
• Remarks on periodic boundary value problems for functional differential equations.
• On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations.
• Existence of multiple solutions for second order boundary value problems
• Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions
• Monotone method for singular Neumann problem
• Monotone iterative technique for impulsive integro-differential equations with periodic boundary conditions
• Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order
• Two-point boundary value problems. Lower and upper solutions
• Existence of at least three solutions of a second-order three-point boundary value problem
• Monotone iterative method for first-order functional difference equations with nonlinear boundary value conditions
• Solvability of three point boundary value problems for second order differential equations with deviating arguments
• Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions
• Existence and uniqueness of solution for fractional differential equations with integral boundary conditions
• Generalized viscoelastic models: their fractional equations with solutions
• Differential Equations of Non-Integer Order

This page was built for publication: Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions