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
2018 ◽  
Vol 7 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Chun Li ◽  
Ravi P. Agarwal ◽  
Dong-Lun Wu

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.


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Huashui Zhan

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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