Nontriviality of some classes of periodic functions of the type of infinite-order Sobolev spaces

1984 ◽  
pp. 21-23
Author(s):  
L. I. Klenina
Keyword(s):  
Sobolev Spaces ◽  
Infinite Order ◽  
Periodic Functions

Sobolev spaces of infinite order

1991 ◽  
Vol 46 (6) ◽  
pp. 107-147 ◽  
Author(s):  
Yu A Dubinskii
Keyword(s):  
Sobolev Spaces ◽  
Infinite Order

scholarly journals Anisotropic nonlinear problem of infinite order with variables exponents and $L^1$ data

2020 ◽  
Author(s):  
Moussa Chrif ◽  
hakima ouyahya
Keyword(s):  
Nonlinear Equation ◽  
Elliptic Operator ◽  
Nonlinear Problem ◽  
Sobolev Spaces ◽  
Lower Order ◽  
Infinite Order ◽  
Existence Of Solutions ◽  
Order Term ◽  
Strongly Nonlinear ◽  
Sign Condition

In this paper, we prove the existence of solutions for the strongly nonlinear equation of the type $$Au+g(x,u)=f$$ where $A$ is an elliptic operator of infinite order from a functional Sobolev spaces of infinite order with variables exponents to its dual. $g(x, s)$ is a lower order term satisfying essentially a sign condition on s and the second term f belongs to $L^1(\Omega)$.

Elliptic equations in weighted Sobolev spaces of infinite order with L 1 data

2009 ◽  
Vol 33 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Mostafa Bendahmane ◽  
Moussa Chrif ◽  
Said El Manouni
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Infinite Order ◽  
Weighted Sobolev Spaces
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