Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

1996 ◽  
Author(s):  
Thomas Runst ◽  
Winfried Sickel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Sobolev Spaces ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Nemytskij Operators

scholarly journals Extreme points and rotundity of Orlicz-Sobolev spaces

2002 ◽  
Vol 32 (5) ◽  
pp. 293-299
Author(s):  
Shutao Chen ◽  
Changying Hu ◽  
Charles Xuejin Zhao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Necessary Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Extreme Points ◽  
Necessary Condition ◽  
Partial Differential ◽  
Sufficient And Necessary Conditions ◽  
Sufficient And Necessary Condition

It is well known that Sobolev spaces have played essential roles in solving nonlinear partial differential equations. Orlicz-Sobolev spaces are generalized from Sobolev spaces. In this paper, we present sufficient and necessary conditions of extreme points of Orlicz-Sobolev spaces. A sufficient and necessary condition of rotundity of Orlicz-Sobolev spaces is obtained.

scholarly journals Solvability of Impulsive Nonlinear Partial Differential Equations with Nonlocal Conditions

2020 ◽  
pp. 140-152
Author(s):  
Ali Kadhim Jabbar ◽  
Sameer Qasim Hasan
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Theoretical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Nonlocal Conditions ◽  
Abstract Cauchy Problem ◽  
Beam Equation ◽  
Partial Differential

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

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