Positive solutions of singular semilinear elliptic problems on unbounded non-smooth domain (Q2923066)

In this paper, the author studies the following nonlinear elliptic problem NEWLINE\[NEWLINE(P)\begin{cases} & \displaystyle\Delta u +\varphi (.,u) = 0 \quad\quad\quad \displaystyle \mathrm{ in } \;\; D,\\ &\displaystyle u(x)>0 \quad\quad\quad\quad\quad\quad\;\;\;\displaystyle \mathrm{in } \;\; D, \\ & \displaystyle \lim_{x\rightarrow z, x\in D}u(x)=0\qquad \quad \;\, \displaystyle \forall z\in \partial D, \end{cases} NEWLINE\]NEWLINE where \(D\) is an unbounded nontangentially accessible domain with a compact boundary \(\partial D\) in \(\mathbb R^n\), \(n\geq 2\). Under suitable conditions on the measurable function \(\varphi\), the author establishes the existence and uniqueness of a positive solution of problem \((P)\).