scholarly journals Uniqueness and existence results for initial value problems on time scales through a reciprocal problem and applications

2009 ◽  
Vol 58 (4) ◽  
pp. 700-710 ◽  
Author(s):  
Victoria Otero-Espinar ◽  
Dolores R. Vivero
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Existence Results ◽  
Initial Value ◽  
Uniqueness And Existence ◽  
Uniqueness And Existence Results

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

scholarly journals Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

2001 ◽  
Vol 32 (4) ◽  
pp. 315-325
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Second Order ◽  
Initial Value ◽  
Functional Differential ◽  
Condensing Maps

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

Existence Results on Infinite Intervals for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces

2000 ◽  
Vol 7 (4) ◽  
pp. 609-625 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Banach Spaces ◽  
Initial Value Problems ◽  
Mild Solutions ◽  
Existence Results ◽  
Topological Spaces ◽  
Initial Value ◽  
Infinite Intervals ◽  
Functional Differential ◽  
The Fixed Point Theorem ◽  
Locally Convex

Abstract In this paper we investigate the existence of mild solutions, on infinite intervals, to initial value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall rely on the fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem.

Uniqueness Implies Existence and Uniqueness Conditions for a Class of (k + j)-Point Boundary Value Problems for n-th Order Differential Equations

2012 ◽  
Vol 55 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Paul W. Eloe ◽  
Johnny Henderson ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Existence Results ◽  
Point Boundary ◽  
Uniqueness And Existence ◽  
Uniqueness And Existence Results

AbstractFor the n-th order nonlinear differential equation, y(n) = f (x, y, y′, … , y(n–1)), we consider uniqueness implies uniqueness and existence results for solutions satisfying certain (k + j)-point boundary conditions for 1 ≤ j ≤ n – 1 and 1 ≤ k ≤ n – j. We define (k; j)-point unique solvability in analogy to k-point disconjugacy and we show that (n – j0; j0)-point unique solvability implies (k; j)-point unique solvability for 1 ≤ j ≤ j0, and 1 ≤ k ≤ n – j. This result is analogous to n-point disconjugacy implies k-point disconjugacy for 2 ≤ k ≤ n – 1.

scholarly journals Existence-uniqueness of solutions for fuzzy nabla initial value problems on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
R. Leelavathi ◽  
G. Suresh Kumar ◽  
M. S. N. Murty ◽  
R. V. N. Srinivasa Rao
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions
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