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Existence and Asymptotic Behavior of Positive Solutions for Variable Exponent Elliptic Systems
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- Journal:
- Advances in Applied Mathematics and Mechanics / Volume 8 / Issue 1 / February 2016
- Published online by Cambridge University Press:
- 21 December 2015, pp. 19-36
- Print publication:
- February 2016
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In this paper, our main purpose is to establish the existence of positive solution of the following system
where 
are constants. F(x,u,υ) = λp(x)[g(x)a(u)+f(υ)], H(x,u,υ)=θq(x)[g1(x)b(υ)+h(u)], λ, θ>0 are parameters, p(x), q(x) are radial symmetric functions, 
is called p(x)-Laplacian. We give the existence results and consider the asymptotic behavior of the solutions. In particular, we do not assume any symmetric condition, and we do not assume any sign condition on F(x,0,0) and H(x,0,0) either.
are constants. 
is called Sub-supersolutions in a variational inequality related to a sandpile problem
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- Journal:
- The ANZIAM Journal / Volume 48 / Issue 2 / October 2006
- Published online by Cambridge University Press:
- 17 February 2009, pp. 179-197
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