scholarly journals Degenerated and Competing Dirichlet Problems with Weights and Convection

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 271
Author(s):  
Dumitru Motreanu
Keyword(s):  
Dirichlet Boundary ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Convection Term ◽  
Dirichlet Problems ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Nemytskij Operators ◽  
First Time

This paper focuses on two Dirichlet boundary value problems whose differential operators in the principal part exhibit a lack of ellipticity and contain a convection term (depending on the solution and its gradient). They are driven by a degenerated (p,q)-Laplacian with weights and a competing (p,q)-Laplacian with weights, respectively. The notion of competing (p,q)-Laplacians with weights is considered for the first time. We present existence and approximation results that hold under the same set of hypotheses on the convection term for both problems. The proofs are based on weighted Sobolev spaces, Nemytskij operators, a fixed point argument and finite dimensional approximation. A detailed example illustrates the effective applicability of our results.

Upper semicontinuity of Nemytskij operators

1991 ◽  
Vol 160 (1) ◽  
pp. 321-330 ◽  
Author(s):  
A. Cellina ◽  
A. Fryszkowski ◽  
T. Rzezuchowski
Keyword(s):  
Upper Semicontinuity ◽  
Nemytskij Operators

scholarly journals On Fréchet-differentiability of Nemytskij operators acting in Hölder spaces

1991 ◽  
Vol 33 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Manfred Goebel
Keyword(s):  
Nonlinear Analysis ◽  
Function Space ◽  
Rich Source ◽  
Hölder Spaces ◽  
Survey Paper ◽  
Superposition Operators ◽  
Fréchet Differentiability ◽  
Nemytskij Operators ◽  
Holder Spaces ◽  
Crucial Part

In any field of nonlinear analysis Nemytskij operators, the superposition operators generated by appropriate functions, play a crucial part. Their analytic properties depend on the postulated properties of the defining function and on the function space in which they are considered. A rich source for related questions is the monograph by J. Appell and P. P. Zabrejko [2] and the survey paper by J. Appell [1].

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