Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in

2008 ◽  
Vol 68 (4) ◽  
pp. 956-968 ◽  
Author(s):  
Xianchun Xu ◽  
Yukun An
Keyword(s):  
Growth Condition ◽  
Elliptic Systems ◽  
Multiplicity Of Solutions ◽  
Nonstandard Growth ◽  
Existence And Multiplicity ◽  
Nonstandard Growth Condition

scholarly journals Existence and multiplicity of solutions for a class of superlinear elliptic systems

2018 ◽  
Vol 7 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Chun Li ◽  
Ravi P. Agarwal ◽  
Dong-Lun Wu
Keyword(s):  
Critical Point ◽  
Growth Condition ◽  
Critical Point Theory ◽  
Elliptic Systems ◽  
Point Theory ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Minimax Methods

AbstractIn this paper, we establish the existence and multiplicity of solutions for a class of superlinear elliptic systems without Ambrosetti and Rabinowitz growth condition. Our results are based on minimax methods in critical point theory.

scholarly journals On Solutions of a Parabolic Equation with Nonstandard Growth Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Huashui Zhan
Keyword(s):  
Parabolic Equation ◽  
Growth Condition ◽  
Boundary Value ◽  
Growth Conditions ◽  
Boundary Value Condition ◽  
Nonstandard Growth ◽  
Partial Boundary Value Condition ◽  
Nonstandard Growth Condition ◽  
Nonstandard Growth Conditions ◽  
The Stability

A parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The stability of weak solutions is based on a natural partial boundary value condition. Two novelty elements of the paper are both the dependence of diffusion coefficient bx,t on the time variable t, and the partial boundary value condition based on a submanifold of ∂Ω×0,T. How to overcome the difficulties arising from the nonstandard growth conditions is another technological novelty of this paper.

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