Sturm type problems for singular \(p\)-Laplacian boundary value problems.
The author considers the following singular boundary value problem for the \(p\)-Laplacian operator: \(L_{p}u+\lambda c(t)u^{ (p-1)}=0\), \(0<t<1\), \(u(0)=u(1)=0\). Here, \(L_{p}u(t)=(a(t)u^{(p-1)})'\). The functions \(a^{-1}\) and \(c\) may be singular at t=0 and/or t=1. It is shown that there exists an increasing sequence of eigenvalues with a description of the corresponding eigenfunctions. As an application the author proves the existence of at least one solution for the nonresonance problem: \(L_{p}u(t)+f(t,u)=0\), \(u(0)=u(1)=0\).
scientific article; zbMATH DE number 1861380