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Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

Proving uniqueness for the solution of the problem of homogeneous and anisotropic micropolar thermoelasticity

In this paper we derive some identities for the solution of the problem of homogeneous and anisotropic micropolar thermoelasticity. These can be applied to proving uniqueness of the solution of the corresponding boundary initial value problem.

New applications of Calvert and Gupta’s results to hyperbolic differential equation with mixed boundaries

Calvert and Gupta’s results concerning the perturbations on the ranges of m-accretive mappings have been employed widely in the discussion of the existence of solutions of nonlinear elliptic differential equation with Neumann boundary. In this paper, we shall focus our attention on certain hyperbolic differential equation with mixed boundaries. By defining some suitable nonlinear...

Positive solutions of higher-order Sturm-Liouville boundary value problems with derivative-dependent nonlinear terms

We consider the Sturm-Liouville boundary value problem { y ( m ) ( t ) + F ( t , y ( t ) , y ′ ( t ) , … , y ( q ) ( t ) ) = 0 , t ∈ [ 0 , 1 ] , y ( k ) ( 0 ) = 0 , 0 ≤ k ≤ m − 3 , ζ y ( m − 2 ) ( 0 ) − θ y ( m − 1 ) ( 0 ) = 0 , ρ y ( m − 2 ) ( 1 ) + δ y ( m − 1 ) ( 1 ) = 0 , where m ≥ 3 and 1 ≤ q ≤ m − 2 . We note that the nonlinear term F involves derivatives. This makes the...

Nonconstant periodic solutions for a class of ordinary p-Laplacian systems

In this paper, we study the existence of periodic solutions for a class of ordinary p-Laplacian systems. Our technique is based on the generalized mountain pass theorem of Rabinowitz. MSC: 47J30, 34B15, 34C25, 35B38.

Existence results for sequential fractional integro-differential equations with nonlocal multi-point and strip conditions

In this paper we investigate a new kind of nonlocal multi-point boundary value problem of Caputo type sequential fractional integro-differential equations involving Riemann-Liouville integral boundary conditions. Several existence and uniqueness results are obtained via suitable fixed point theorems. Some illustrative examples are also presented. The paper concludes with some...

Fractional differential equations and inclusions with semiperiodic and three-point boundary conditions

In this article, we investigate the existence of solutions for boundary value problems of fractional differential equations and inclusions with semiperiodic and three-point boundary conditions. The existence results for equations are obtained by applying Banach’s contraction mapping principle, Schaefer-type fixed point theorem, Leray-Schauder degree theory, Krasnoselskii’s fixed...

Study on the generalized ( p , q ) -Laplacian elliptic systems, parabolic systems and integro-differential systems

In this paper, we present the abstract results for the existence and uniqueness of the solution of nonlinear elliptic systems, parabolic systems and integro-differential systems involving the generalized ( p , q ) -Laplacian operator. Our method makes use of the characteristics of the ranges of linear and nonlinear maximal monotone operators and the subdifferential of a proper...

Existence results for fractional differential equations of arbitrary order with nonlocal integral boundary conditions

In this paper, we investigate the existence of solutions for fractional differential equations of arbitrary order with nonlocal integral boundary conditions. The existence results are obtained by applying Krasnoselskii’s fixed point theorem and Leray-Schauder degree theory, while the uniqueness of the solutions is established by means of Banach’s contraction mapping principle...

A nonlinear equation for fluids in multiconnected domain

In this paper we propose a mathematical model for Reynolds’ equation of a compressible fluid on a multiconnected field which simulates the function of a hybrid bearing. The boundary conditions on the inner boundaries are derived from the flow-rate continuity through the supplying orifices and are expressed by means of an integro-differential nonlinear equation. We propose a...

Some new versions of fractional boundary value problems with slit-strips conditions

We discuss the existence and uniqueness of solutions for a fractional differential equation of order q ∈ ( n − 1 , n ] with slit-strips type boundary conditions. The slit-strips type boundary condition states that the sum of the influences due to finite strips of arbitrary lengths is related to the value of the unknown function at an arbitrary position (nonlocal point) in the...

New method for the existence and uniqueness of solution of nonlinear parabolic equation

There are two contributions in this paper. The first is that the abstract result for the existence of the unique solution of certain nonlinear parabolic equation is obtained by using the properties of H-monotone operators, consequently, the proof is simplified compared to the corresponding discussions in the literature. The second is that the connections between resolvent of H...

Existence of solutions to fourth-order differential equations with deviating arguments

In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u ( 4 ) ( t ) + q ( t ) f ( t , [ u ( t ) ] , [ u ′ ( t ) ] , [ u ″ ( t ) ] , u ‴ ( t ) ) = 0 , 0 < t < + ∞ , with the boundary conditions u ( 0 ) = A , u ′ ( 0 ) = B , u ″ ( t ) − a u ‴ ( t ) = θ ( t ) , − τ ≤ t ≤ 0 ; u ‴ ( + ∞ ) = C . We present sufficient...

Multiplicity and uniqueness results for the singular nonlocal boundary value problem involving nonlinear integral conditions

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign.

Periodic and subharmonic solutions for a class of second-order p-Laplacian Hamiltonian systems

In this paper, the periodic and subharmonic solutions are investigated for a class of second-order non-autonomous ordinary differential equations with a p-Laplacian. With the perturbation technique and the dual least action principle, some existence results are given of solutions to the convex p-Laplacian systems.

Upper and lower solution method for nth-order BVPs on an infinite interval

This work is devoted to the study of nth-order ordinary differential equations on a half-line with Sturm-Liouville boundary conditions. The existence results of a solution, and triple solutions, are established by employing a generalized version of the upper and lower solution method, the Schäuder fixed point theorem, and topological degree theory. In our problem the nonlinearity...

Method of quasilinearization for a nonlocal singular boundary value problem in weighted spaces

This paper studies the existence and uniqueness of solutions for a nonlocal singular boundary value problem of second-order integro-differential equations in weighted spaces. The method of quasilinearization is applied to obtain monotone sequences of approximate solutions converging uniformly and quadratically to a unique solution of the problem at hand. An illustrative example...

Effect of intrinsic rotations, microstructural expansion and contractions in initial boundary value problem of thermoelastic bodies

This study is dedicated to some basic theorems in the thermoelastodynamics of microstretch bodies. Our intention is to show that the presence of the microstretch does not affect the main characteristics of the mixed initial boundary value problem for thermoelastic bodies. The result regarding the uniqueness theorem is derived with no definiteness assumptions on the elastic...