Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition

2012 ◽  
Vol 57 (5) ◽  
pp. 579-595 ◽  
Author(s):  
R.A. Mashiyev ◽  
B. Cekic ◽  
M. Avci ◽  
Z. Yucedag
Keyword(s):  
Growth Condition ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nonstandard Growth ◽  
Existence And Multiplicity ◽  
Nonstandard Growth Condition

scholarly journals Multivalued elliptic operators with nonstandard growth

2018 ◽  
Vol 7 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Mustafa Avci ◽  
Alexander Pankov
Keyword(s):  
Exact Solution ◽  
Dirichlet Problem ◽  
Growth Condition ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Approximate Solutions ◽  
Growth Conditions ◽  
Lavrentiev Phenomenon ◽  
Nonstandard Growth ◽  
Nonstandard Growth Condition

AbstractThe paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic equations with nonstandard growth condition. The growth conditions are more general than the well-known {p(x)} growth. Moreover, we allow the presence of the so-called Lavrentiev phenomenon. As consequence, at least two types of variational settings of Dirichlet problem are available. We prove results on the existence of solutions in both of these settings. Then we obtain several results on the convergence of certain types of approximate solutions to an exact solution.

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.

Sign in / Sign up

Export Citation Format

Share Document