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We propose a new approach to the study of Sturm–Liouville problems nonlinear in thespectral parameter. The approach is based on the introduction of a transcendental functionrelated to the problem under study, called the integral characteristic function, which determinesthe eigenvalues of the Sturm–Liouville problem in question. The study of this function permitsone to prove the solvability of the problem, find the eigenvalue asymptotics, obtain comparisontheorems, and introduce a natural numbering of the eigenvalues and zeros of the eigenfunctions.We use this approach to study a nonlinear Sturm–Liouville problem on an interval with boundaryconditions of the first kind.
Differential Equations – Springer Journals
Published: Dec 1, 2021
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