181 papers found.

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By using fixed point results on cones, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Examples are presented in order to illustrate the obtained results.

The present paper is framed to study weak, strong and strict converse duality relations for a semi-infinite programming problem and its Wolfe and Mond-Weir-type dual programs under generalized (Hp,r)-invexity.MSC: 90C32, 49K35, 49N15.

We consider the following complementary Lidstone boundary value problem ( - 1 ) m y ( 2 m + 1 ) ( t ) = λ F ( t , y ( t ) , y ′ ( t ) ) , t ∈ ( 0 , 1 ) y ( 0 ) = 0 , y ( 2 k - 1 ) ( 0 ) = y ( 2 k - 1 ) ( 1 ) = 0 , 1 ≤ k ≤ m where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such...

Some new criteria for the oscillation of n th order nonlinear dynamic equations of the form x Δ n t + q t x σ ξ t λ = 0 are established in delay ξ(t) ≤ t and non-delay ξ(t) = t cases, where n ≥ 2 is a positive integer, λ is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as...

**Ravi** **P** **Agarwal**
0
Maryam A Alghamdi
Naseer Shahzad
nshahzad@kau
0
0
Department of Mathematics, King Abdulaziz University
, P.O. Box 80203, Jeddah 21859,
Saudi Arabia
In this article, we give some

Chenghui Zhang
0
**Ravi** **P** **Agarwal**
Martin Bohner
Tongxing Li
0
0
School of Control Science and Engineering, Shandong University
,
Jinan, Shandong 250061
,
P.R. China
Some new results are presented for

In this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. To illustrate our abstract results, an example is given. MSC: 35A05, 34G20, 34K05, 26A33.

We tackle the existence and uniqueness of the solution for a kind of integro-differential equations involving the generalized p-Laplacian operator with mixed boundary conditions. This is achieved by using some results on the ranges for maximal monotone operators and pseudo-monotone operators. The method used in this paper extends and complements some previous work.MSC: 47H05, 47H09.

In this paper, we study the existence of solutions for Riemann-Liouville type integro-differential equations of fractional order α ∈ ( 2 , 3 ] with nonlocal three-point fractional boundary conditions via Sadovskii’s fixed point theorem for condensing maps. An illustrative example is also presented. MSC:34A08, 34B10, 34B15.

In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains. Our results are extensions of Lp norm inequalities for Green's operator and can be used to estimate the norms of other operators applied to differential forms. 2000 Mathematics Subject...

This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also...

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series...

This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also...

This article studies the existence and dimension of the set for mild solutions of semilinear fractional differential inclusions. We recall and prove some new results on multivalued maps to establish our main results. MSC 2010: 34A12; 34A40.

Received 5 March 2012; Accepted 20 June 2012
Academic Editor: Simeon Reich
Copyright © 2012 **Ravi** **P**. **Agarwal** et al. This is an open access article distributed under the Creative Commons Attribution

Received 5 March 2012; Accepted 20 June 2012
Academic Editor: Simeon Reich
Copyright © 2012 **Ravi** **P**. **Agarwal** et al. This is an open access article distributed under the Creative Commons Attribution

In this paper, we study the existence of solutions for Riemann-Liouville type integro-differential equations of fractional order α ∈ ( 2 , 3 ] with nonlocal three-point fractional boundary conditions via Sadovskii’s fixed point theorem for condensing maps. An illustrative example is also presented.MSC: 34A08, 34B10, 34B15.

Some new criteria for the oscillation of nth order nonlinear dynamic equations of the form x Δ n t + q t x σ ξ t λ = 0 are established in delay ξ(t) ≤ t and non-delay ξ(t) = t cases, where n ≥ 2 is a positive integer, λ is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as...

The Sumudu transform of certain elementary matrix functions is obtained. These transforms are then used to solve the differential equation of a general linear conservative vibration system, a vibrating system with a special type of viscous damping.

Manuel De la Sen
**Ravi** **P** **Agarwal**
This article discusses three weak -contractive conditions of rational type for a class of 2-cyclic self-mappings defined on the union of two non-empty subsets of a