An elliptic equation with an indefinite sublinear boundary condition
Humberto Ramos Quoirin, Kenichiro Umezu · Advances in Nonlinear Analysis · 2016
Abstract We investigate the problem { - Δ u = | u | p - 2 u in Ω , ∂ u ∂ 𝐧 = λ b ( x ) | u | q - 2 u on ∂ Ω , \left\{\begin{aligned} \displaystyle-\Delta u&\displaystyle=\lvert u\rvert^{p-% 2}u&&\displaystyle\phantom{}\text{in ${\Omega}$},\\ \displaystyle\frac{\partial u}{\partial\mathbf{n}}&\displaystyle=\lambda b(x)% \lvert u\rvert^{q-2}u&&\displaystyle\phantom{}\text{on ${\partial\Omega}$},% \end{aligned}\right. where Ω is a bounded and smooth domain of ℝ N {\mathbb{R}^{N}} ( N ≥ 2 {N\geq 2} ), 1 < q < 2 < p {1 , λ