Existence of a positive solution for one-dimensional singular \(p\)-Laplacian problems and its parameter dependence
The authors consider consider one-dimensional singular \(p\)-Laplacian problem \[ \lambda (\varphi_p(u'))'+w(t)f(t,u) = 0, \] \[ au(0)- bu'(0) =\int^1_0 g(t)u(t)dt, u'(1) = 0, \] where \(\lambda\) is a positive parameter, \(p(s) = |s|^{p-2}s\), \(p > 1\), and \(w\) may be singular at \(t = 0\) and/or \(t = 1\). Using fixed-point techniques, they establish some existence, multiplicity, and nonexistence results. They also study the dependence of the positive solution \(u_\lambda(t)\) on the parameter \(\lambda\).
scientific article; zbMATH DE number 6420280
scientific article