Multiple eigenvalues of a one-dimensional quasilinear problem
The authors define and analyze eigenvalue problems of second-order quasilinear differential equations in the one-dimensional formulation. A quadrature expression is derived for the inverse \(x(u)\) of the eigenfunctions \(u(x)\). A technique is developed for the study of the spectrum, which depends on the form of the nonlinearity \(f(u)\). Special attention is given to functions \(f(u)\) generating problems with multiple eigenvalues and several positive eigenfunctions. Seven versions of problems are analyzed. Future research should extend results to multidimensional formulations.
scientific article; zbMATH DE number 5998401