Radial solutions for a nonlinear problem with \(p\)-Laplacian
This paper concerns nonlinear singular boundary value problems of the type \[ [t^a|y'(t)|^b y'(t)]'= t^a g(t, y(t), y'(t)),\;t\in I= (0, 1], \quad y(1)= 0= \lim_{t\to 0+} y'(t),\tag{1} \] for constants \(a> 0\), \(b> -1\). Under various technical conditions on the function \(g\), the main theorems establish the existence of bounded solutions, positive decreasing solutions, and negative increasing solutions \(y\in C^1(I)\) or \(y\in C^1(\overline I)\) of problem (1). The proofs involve the Schauder-Tychonov fixed-point theorem. For \(a= n- 1\), \(n\geq 2\), the results are applicable to radial \(p\)-Laplacian Dirichlet problems in the unit ball in \(\mathbb{R}^n\).
nonliner singular boundary value problems
radial \(p\)-Laplacian Dirichlet problems
scientific article; zbMATH DE number 896477