scholarly journals Geometric and analytic views in existence theorems for optimal control in Banach spaces. Part 1. Distributed parameters

1974 ◽  
Vol 14 (5) ◽  
pp. 505-520 ◽  
Author(s):  
L. Cesari
Keyword(s):  
Optimal Control ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Distributed Parameters

scholarly journals Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations

2000 ◽  
Vol 158 ◽  
pp. 73-86
Author(s):  
Jinqing Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Maximal And Minimal Solutions

AbstractIn this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.

scholarly journals Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Banach Space ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Existence Theorems ◽  
Integrodifferential Equations ◽  
Existence Theory

We prove existence theorems for the integrodifferential equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values in a Banach spaceEand the integral is taken in the sense of HL. Additionally, the functionsfandksatisfy certain boundary conditions expressed in terms of the measure of noncompactness.

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