On a pseudo Fučik spectrum for strongly nonlinear second-order ODEs and an existence result
The authors study the boundary value problem of the form \((\varphi (u'))' + f(t,u) = q(t)\), \(u(a) = u(b) = 0\), where \(\varphi\) is an increasing odd homeomorphism of \(R\), \(f\) and \(q\) satisfy the Carathéodory conditions. The main existence result is formulated in terms of the pseudo Fučik spectrum for the eigenvalue-like problem \((\varphi (u'))' + A \varphi (u^ +) - B \varphi (u^ -) = 0\), \(u(a) = u(b) = 0\), \(A,B > 0\).
scientific article; zbMATH DE number 711768