Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-07-07 , DOI: 10.1142/s0219199720500273
João Pablo Pinheiro da Silva; Claudionei Pereira de Oliveira

In this work, we study the following problem $(𝒫)−Δu=λg(x)u+12∗f(x)Hu(u,v),inℝN,−Δv=μh(x)v+12∗f(x)Hv(u,v),inℝN,$ where $N≥4$, $2∗:=2N/(N−2)$, $Hu$ and $Hv$ are the partial derivatives of the homogeneous function $H∈C1(ℝ+2,ℝ)$, where $ℝ+2=[0,∞)×[0,∞)$, $g+≢0$, $h+≢0$, $f+≢0$, $g,h,f∈L∞(ℝN)$, $g+,h+∈LN/2(ℝN)$ and $λ,μ>0$.

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