scholarly journals A global existence theorem for autonomous differential equations in a Banach space

1970 ◽  
Vol 26 (2) ◽  
pp. 307-307 ◽  
Author(s):  
R. H. Martin
Keyword(s):  
Banach Space ◽  
Global Existence ◽  
Differential Equations ◽  
Existence Theorem ◽  
Global Existence Theorem ◽  
Autonomous Differential Equations

scholarly journals GLOBAL REGULAR SOLUTION FOR THE EINSTEIN-MAXWELL-BOLTZMANN-SCALAR FIELD SYSTEM IN A BIANCHI TYPE-I SPACE-TIME

2017 ◽  
Vol 13 (1) ◽  
pp. 7087-7118 ◽  
Author(s):  
Noutchegueme Norbert
Keyword(s):  
Scalar Field ◽  
Global Existence ◽  
Cosmological Constant ◽  
Existence Theorem ◽  
Regular Solution ◽  
Existence And Uniqueness ◽  
Bianchi Type ◽  
Type I ◽  
Field System ◽  
Global Existence Theorem

We prove an existence and uniqueness of regular solution to the Einstein-Maxwell-Boltzmann-Scalar Field system with pseudo-tensor of pressure and the cosmological constant globaly in time. We clarify the choice of the function spaces and we establish step by step all the essential energy estimations leading to the global existence theorem.

On the Diffeomorphisms Between Banach and Hilbert Spaces

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Dariusz Idczak ◽  
Andrzej Skowron ◽  
Stanislaw Walczak
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Differential Equations ◽  
Existence Theorem ◽  
Hilbert Spaces ◽  
Mountain Pass Theorem ◽  
Sufficient Conditions ◽  
Mountain Pass ◽  
Final Part

AbstractIn this paper, we give some sufficient conditions for f : X → H to be a diffeomorphism, where X is a Banach space and H is a Hilbert space. The proof of the result is based on the mountain pass theorem. Using this result, in the final part of the paper, we prove an existence theorem for some class of integro-differential equations.

scholarly journals An existence theorem for ordinary differential equations in Banach spaces

1984 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
Bogdan Rzepecki
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Regularity Condition ◽  
Measure Of Noncompactness ◽  
Bounded Solution ◽  
Carathéodory Conditions

We prove the existence of bounded solution of the differential equation y′ = A(t)y + f(t, y) in a Banach space. The method used here is based on the concept of “admissibility” due to Massera and Schäffer when f satisfies the Caratheodory conditions and some regularity condition expressed in terms of the measure of noncompactness α.

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