Existence of positive radial solutions for the \(n\)-dimensional \(p\)-Laplacian (Q5936420)

The authors study the following Dirichlet problem on the unit ball \(B_1\) centered at the origin of \(\mathbb{R}^n\): NEWLINE\[NEWLINE-\Delta_p u=q(|x|)f(u), \quad x\in B_1, \qquad u(x)=0, \quad x\in\partial B_1,NEWLINE\]NEWLINE where the functions \(q:(0,1)\to \mathbb{R}_+\) and \(f:\mathbb{R}\to \mathbb{R}\) are continuous, and \(\Delta_p\), \(p>1\), denotes the \(p\)-Laplacian. Under some geometric assumptions on the graph of the nonlinearity \(f\), that do not take into account the behaviour near \(0\) and at infinity of \(f\), the authors prove an existence and localization result for positive radial solutions. The proof is based on the Schauder fixed-point theorem.