Advanced search    

Search: authors:"Ravi P. Agarwal"

44 papers found.
Use AND, OR, NOT, +word, -word, "long phrase", (parentheses) to fine-tune your search.

Positive solutions for a system of second-order discrete boundary value problems

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to multi-point boundary conditions, under some assumptions on the nonlinearities of the system which contains concave functions. In the proofs of our main results we use some theorems from the fixed point index theory.

Birth, growth and computation of pi to ten trillion digits

Ravi P Agarwal 0 Hans Agarwal Syamal K Sen 0 Department of Mathematics, Texas A&M University-Kingsville , Kingsville, TX , 78363, USA The universal real constant pi, the ratio of the circumference ... businesswoman, Sky Silvestry mimics the speech of The Doctor by repeating the square root of to decimal places .. . Syamal K. Sen and Ravi P. Agarwal suggested four Matlab based procedures, viz, (i) Exhaustive

Existence results for multi-term fractional differential equations with nonlocal multi-point and multi-strip boundary conditions

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and multi-strip boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples. Some new results are also deduced by fixing the parameters involved in the...

A matched space for time scales and applications to the study on functions

In this paper, using the algebraic structure of the Abelian group, we introduce the concept of a matched space for time scales, and we construct the algebraic structure of matched spaces to solve the closedness of time scales under non-translational shifts. Using a matched space for time scales, a new concept of periodic time scales is introduced. Based on it, new concepts of...

Compactness criteria and new impulsive functional dynamic equations on time scales

P Agarwal 1 Donal O'Regan 0 0 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland , Galway , Ireland 1 Department of Mathematics, Texas A&M University-Kingsville

Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations

In this paper, we use the analysis of relatively dense sets to point out some deficiencies and inaccuracies in the definition of uniformly almost periodic functions which has been proposed in recent works, and we correct it. Some new generalizations of invariance under translation time scales and almost periodic functions are established. Our study will ensure that now we can...

Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy

Chao Wang Ravi P Agarwal In this work, we address the periodic coverage phenomenon on arbitrary unbounded time scales and initiate a new idea, namely, we introduce the concept of changing-periodic time

On fractional differential equations and inclusions with nonlocal and average-valued (integral) boundary conditions

This paper is concerned with the existence of solutions for boundary value problems of fractional differential equations and inclusions supplemented with nonlocal and average-valued (integral) boundary conditions. The existence results for the single-valued case (equations) are obtained by means of fixed point theorems due to O’Regan and Sadovski, whereas the existence of...

Hadamard-type fractional functional differential equations and inclusions with retarded and advanced arguments

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for boundary value problems of Hadamard-type fractional functional differential equations and inclusions involving both retarded and advanced arguments. We make use of the standard tools of fixed point theory to obtain the main results. MSC: 34A08, 34K05.

Asymptotics and oscillation of nth-order nonlinear differential equations with p-Laplacian like operators

This paper is concerned with nth-order nonlinear differential equations of the form ( a ( t ) | x ( n − 1 ) ( t ) | p − 2 x ( n − 1 ) ( t ) ) ′ + r ( t ) | x ( n − 1 ) ( t ) | p − 2 x ( n − 1 ) ( t ) + q ( t ) | x ( g ( t ) ) | p − 2 x ( g ( t ) ) = 0 with n ≥ 2 . By discussing the signs of ith-order derivatives of eventually positive solutions, for i = 1 , … , n − 1 , and using...

Structure of the solution set for a partial differential inclusion

In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and nonconvex multivalued perturbations, and obtain an existence theorem on extremal solutions, and a strong relaxation theorem. Also we prove that the solution set is compact...

On the existence of solution for fractional differential equations of order 3 < δ 1 ≤ 4

In this paper, we deal with a fractional differential equation of order δ 1 ∈ ( 3 , 4 ] with initial and boundary conditions, D δ 1 ψ ( x ) = − H ( x , ψ ( x ) ) , D α 1 ψ ( 1 ) = 0 = I 3 − δ 1 ψ ( 0 ) = I 4 − δ 1 ψ ( 0 ) , ψ ( 1 ) = Γ ( δ 1 − α 1 ) Γ ( ν 1 ) I δ 1 − α 1 H ( x , ψ ( x ) ) ( 1 ) , where x ∈ [ 0 , 1 ] , α 1 ∈ ( 1 , 2 ] , addressing the existence of a positive...

Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive ∇-dynamic equations on time scales

In the present paper, by introducing the concept of equipotentially almost automorphic sequence, the concept of weighted piecewise pseudo almost automorphic functions on time scales is proposed. Some first results about their basic properties are obtained and some composition theorems are established. Then we apply these to investigate the existence of weighted piecewise pseudo...

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1):59-73, 2015; Adv. Differ. Equ. 2013:302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces.

Successive iteration and positive extremal solutions for nonlinear impulsive q k -difference equations

This paper investigates the existence of positive extremal solutions for nonlinear impulsive q k -difference equations via a monotone iterative method. The main result is well illustrated with the aid of an example. MSC: 34B37, 39A13.

On Caputo type sequential fractional differential equations with nonlocal integral boundary conditions

Agarwal 0 Bashir Ahmad 0 0 Department of Mathematics, Faculty of Science, King Abdulaziz University , P.O. Box 80203, Jeddah, 21589 , Saudi Arabia This paper investigates a boundary value problem of

The existence of solutions for some fractional finite difference equations via sum boundary conditions

In this manuscript we investigate the existence of the fractional finite difference equation (FFDE) Δμ−2μx(t)=g(t+μ−1,x(t+μ−1),Δx(t+μ−1)) via the boundary condition x(μ−2)=0 and the sum boundary condition x(μ+b+1)=∑k=μ−1αx(k) for order 1<μ≤2, where g:Nμ−1μ+b+1×R×R→R, α∈Nμ−1μ+b, and t∈N0b+2. Along the same lines, we discuss the existence of the solutions for the following FFDE...

Oscillation and nonoscillation for second order neutral dynamic equations with positive and negative coefficients on time scales

Xun-Huan Deng Qi-Ru Wang Ravi P Agarwal We investigate oscillation and nonoscillation of certain second order neutral dynamic equations with positive and negative coefficients. We apply the results

Existence and uniqueness of positive solutions to fractional boundary value problems with nonlinear boundary conditions

In this manuscript, we consider two problems of boundary value problems for a fractional differential equation. A fixed point theorem in partially ordered sets and a contraction mapping principle are applied to prove the existence of at least one positive solution for both fractional boundary value problems.MSC: 47H10, 26A33, 34A08.

Existence of solutions for a coupled system of nonlinear fractional differential equations with fractional boundary conditions on the half-line

In this article, we study a boundary value problem of a coupled system of nonlinear Riemann-Liouville type fractional differential equations with fractional boundary conditions on the half-line. An appropriate compactness criterion is established to prove the existence of solutions of the problem by means of the Schauder fixed point theorem. An illustrative example is also given...