| Abstrakt: |
We study the existence of solutions for the following boundary value problem involving the (p,q)$$ \left(p,q\right) $$‐Laplacian −Δpu=λk(x)|u|p−2u+αα+βa(x)|u|α−2u|v|βinS∖S0,−Δqv=νl(x)|v|q−2v+βα+βa(x)|u|α|v|β−2vinS∖S0,v=u=0inS0.$$ \left\{\begin{array}{llll}-{\Delta}_pu& =\lambda k(x){\left|u\right|}^{p-2}u+\frac{\alpha }{\alpha +\beta }a(x){\left|u\right|}^{\alpha -2}u{\left|v\right|}^{\beta }& in& \mathcal{S}\setminus {\mathcal{S}}_0,\\ {}-{\Delta}_qv& =\nu l(x){\left|v\right|}^{q-2}v+\frac{\beta }{\alpha +\beta }a(x){\left|u\right|}^{\alpha }{\left|v\right|}^{\beta -2}v& in& \mathcal{S}\setminus {\mathcal{S}}_0,\\ {}v=u& =0& in& {\mathcal{S}}_0.\end{array}\right. $$where S$$ \mathcal{S} $$ is the Sierpiński g on ℝN−1$$ {\mathbb{R}}^{N-1} $$ for N≥3,S0$$ N\ge 3,{\mathcal{S}}_0 $$ is its boundary, a,k,l:S→ℝ$$ a,k,l:\mathcal{S}\to \mathbb{R} $$ are appropriate functions and α,β,p$$ \alpha, \beta, p $$ and q$$ q $$ are reals satisfying an adequate hypothesis. [ABSTRACT FROM AUTHOR] |
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