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-Schauder condition , Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 61 ( 1976 ), no. 3-4 , 193 - 194 .
**Ravi** **P**. **Agarwal** : Department of Mathematical Sciences, Florida Institute of Technology

-Schauder condition , Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 61 ( 1976 ), no. 3-4 , 193 - 194 .
**Ravi** **P**. **Agarwal** : Department of Mathematical Sciences, Florida Institute of Technology

special retract of E? provided
we assume (2.9) and replace (2.1) with (2.10).
Remark 2.8. In Theorem 2.6, note (2.11) could be replaced by (2.12).
**Ravi** **P**. **Agarwal**: Department of Mathematical Sciences

Hindawi Publishing Corporation
International Journal of Mathematics and Mathematical Sciences
**RAVI** **P**. **AGARWAL**
JEWGENI H. DSHALALOW
DONAL O'REGAN
New Leray-Schauder alternatives are presented for Mo ... ( 2000 ), no. 2 , 594 - 612 . **Ravi** **P**. **Agarwal**: Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901 -6975, USA E-mail address: Jewgeni H. Dshalalow

Hindawi Publishing Corporation
Journal of Applied Mathematics and Stochastic Analysis
**RAVI** **P**. **AGARWAL** 0
DONAL O'REGAN 0
OLEKSANDR E. ZERNOV 0
0 Donal O'Regan: Department of Mathematics, National ... ? > 0 and ui ? , i ?
{1, 2}. Therefore T : ? is the continuous operator. To complete the proof of the
theorem, it suffices to apply the Schauder fixed point theorem to the operator T : .
?
**Ravi** **P**

special retract of E? provided
we assume (2.9) and replace (2.1) with (2.10).
Remark 2.8. In Theorem 2.6, note (2.11) could be replaced by (2.12).
**Ravi** **P**. **Agarwal**: Department of Mathematical Sciences

Hindawi Publishing Corporation
International Journal of Mathematics and Mathematical Sciences
**RAVI** **P**. **AGARWAL**
JEWGENI H. DSHALALOW
DONAL O'REGAN
New Leray-Schauder alternatives are presented for Mo ... ( 2000 ), no. 2 , 594 - 612 . **Ravi** **P**. **Agarwal**: Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901 -6975, USA E-mail address: Jewgeni H. Dshalalow

Hindawi Publishing Corporation
Journal of Applied Mathematics and Stochastic Analysis
**RAVI** **P**. **AGARWAL** 0
DONAL O'REGAN 0
OLEKSANDR E. ZERNOV 0
0 Donal O'Regan: Department of Mathematics, National ... ? > 0 and ui ? , i ?
{1, 2}. Therefore T : ? is the continuous operator. To complete the proof of the
theorem, it suffices to apply the Schauder fixed point theorem to the operator T : .
?
**Ravi** **P**

**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

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...

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.

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.

In this paper, using fixed-point index theory and approximation techniques, we consider the existence and multiplicity of fixed points of some nonlinear operators with singular perturbation. As an application we consider the existence and multiplicity of positive solutions of singular systems of multi-point boundary value problems, which improve the results in the literature.

This paper investigates the existence and multiplicity of positive solutions of a sixth-order differential system with four variable parameters using a monotone iterative technique and an operator spectral theorem.MSC: 34B15, 34B18.

**Ravi** **P** **Agarwal**
Abdul Sami Awan
Donal O'Regan
Awais Younus
0
1
0
Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. University
,
Multan
,
Pakistan
1
Abdus Salam School of Mathematical

In this paper we present existence and uniqueness results for a class of fuzzy fractional integral equations. To prove the existence result, we give a variant of the Schauder fixed point theorem in semilinear Banach spaces. MSC:34A07, 34A08.

In this paper, we establish some sufficient conditions for ( 2 , 2 ) -disconjugacy and study the distribution of zeros of nontrivial solutions of fourth-order differential equations. The results are extended to cover some boundary value problems in bending of beams. The main results are proved by making use of a generalization of Hardy’s inequality and some Opial-type...

In this paper we establish an existence result for the multi-term fractional differential equation ( D α m − ∑ i = 1 m − 1 a i D α i ) u ( t ) = f ( t , u ( t ) ) for t ∈ [ 0 , 1 ] , u ( 0 ) = 0 , (1) where D p α m y ( ⋅ ) and D p α i y ( ⋅ ) are fractional pseudo-derivatives of a weakly absolutely continuous and pseudo-differentiable function u ( ⋅ ) : T → E of order α m and...

In this paper we establish an existence result for the multi-term fractional differential equation (Dαm−∑i=1m−1aiDαi)u(t)=f(t,u(t))for t∈[0,1],u(0)=0, where Dpαmy(⋅) and Dpαiy(⋅) are fractional pseudo-derivatives of a weakly absolutely continuous and pseudo-differentiable function u(⋅):T→E of order αm and αi, i=1,2,…,m−1, respectively, the function f(t,⋅):T×E→E is weakly-weakly...

In this article, we consider the following systems of Fredholm integral equations: u i ( t ) = h i ( t ) + ∫ 0 T g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , T ] , 1 ≤ i ≤ n , u i ( t ) = h i ( t ) + ∫ 0 ∞ g i ( t , s ) f i ( s , u 1 ( s ) , u 2 ( s ) , … , u n ( s ) ) d s , t ∈ [ 0 , ∞ ) , 1 ≤ i ≤ n . Using an argument originating from Brezis...