JournalszaaVol. 41, No. 1/2pp. 49–64

Monotonicity results for quasilinear fractional systems in epigraphs

  • Phuong Le

    University of Economics and Law, Ho Chi Minh City, Vietnam
Monotonicity results for quasilinear fractional systems in epigraphs cover
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Abstract

We prove the monotonicity of positive solutions to the quasilinear fractional system

{(−Δ)psu=f(x,u,v)in Ω,(−Δ)qtv=g(x,u,v)in Ω,u=v=0in Rn∖Ω,\begin{cases} (-\Delta)^s_p u = f(x,u,v) &\text{in } \Omega,\\ (-\Delta)^t_q v = g(x,u,v) &\text{in } \Omega,\\ u=v=0 &\text{in } \mathbb{R}^n\setminus \Omega, \end{cases}

where Ω\Omega is a coercive or non-coercive epigraph, such as the halfspace R+n\mathbb{R}^n_+, 0<s,t<10<s,t<1 and p,q≥2p,q\ge2. By combining a new decay at infinity principle with the direct method of moving planes, we improve recent works in the literature even in the case of a single equation.

Cite this article

Phuong Le, Monotonicity results for quasilinear fractional systems in epigraphs. Z. Anal. Anwend. 41 (2022), no. 1/2, pp. 49–64

DOI 10.4171/ZAA/1693