Existence of positive solutions for \(m\)-Laplacian boundary value problems
The author gives some sufficient conditions for the existence of positive solutions to the boundary value problem \[ (|u'(t) |^{m-2}u'(t))' + f(t,u(t)) = 0, \quad 0 < t < 1, \quad u'(0) = u(1) = 0, \] with \(m \geq 2\), \(f: [0,1) \times (0,\infty) \rightarrow (0,\infty)\) is locally Lipschitz continuous and \(f(t,u)/u^{m-1}\) is strictly decreasing in \(u\), for each fixed \(t\). The proofs are based on the shooting method.
scientific article; zbMATH DE number 1369365
scientific article