Schauder's theorem and Riesz theory for compact-like operators

1986 ◽  
Vol 192 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Carl L. DeVito ◽  
Ana M. Suchanek
Keyword(s):  
Schauder’S Theorem

scholarly journals On Riesz operators

1969 ◽  
Vol 16 (3) ◽  
pp. 227-232 ◽  
Author(s):  
J. C. Alexander
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Operators ◽  
Image Position ◽  
Schauder’S Theorem

In (4) Vala proves a generalization of Schauder's theorem (3) on the compactness of the adjoint of a compact linear operator. The particular case of Vala's result that we shall be concerned with is as follows. Let t1 and t2 be non-zero bounded linear operators on the Banach spaces Y and X respectively, and denote by 1T2 the operator on B(X, Y) defined by

scholarly journals On the existence of bounded solutions of nonlinear elliptic systems

2002 ◽  
Vol 30 (8) ◽  
pp. 479-490
Author(s):  
Abdelaziz Ahammou
Keyword(s):  
Compact Operator ◽  
Elliptic System ◽  
Elliptic Systems ◽  
Invariant Set ◽  
Bounded Solutions ◽  
Nonlinear Elliptic Systems ◽  
Shooting Technique ◽  
Nonlinear Elliptic ◽  
Schauder’S Theorem

We study the existence of bounded solutions to the elliptic system−Δpu=f(u,v)+h1inΩ,−Δqv=g(u,v)+h2inΩ,u=v=0on∂Ω, non-necessarily potential systems. The method used is a shooting technique. We are concerned with the existence of a negative subsolution and a nonnegative supersolution in the sense of Hernandez; then we construct some compact operatorTand some invariant setKwhere we can use the Leray Schauder's theorem.

scholarly journals Existence of a solution of a Fourier nonlocal quasilinear parabolic problem

1992 ◽  
Vol 5 (1) ◽  
pp. 43-67 ◽  
Author(s):  
Ludwik Byszewski
Keyword(s):  
Heat Conduction ◽  
Classical Solution ◽  
Parabolic Problem ◽  
Classical Theorem ◽  
Existence Of A Solution ◽  
Quasilinear Parabolic Problem ◽  
Schauder’S Theorem ◽  
Quasilinear Parabolic

The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder's theorem is used. The paper is a continuation of papers [1]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

Stabilities in FDEs by Schauder's theorem

2005 ◽  
Vol 63 (5-7) ◽  
pp. e217-e224 ◽  
Author(s):  
Tetsuo Furumochi
Keyword(s):  
Schauder’S Theorem
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