Geodesic
Existence of solutions of a~nonlinear eigenvalue problem and their properties
Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 52-73

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An eigenvalue problem is considered for a nonlinear nonautonomous ordinary differential equation of the second order on a closed interval with conditions of the first type and an additional (local) condition. The nonlinearity in the equation is due to a monotonically increasing nonnegative function with powerlike growth at infinity. The existence of infinite numbers of negative and positive eigenvalues is shown. Asymptotic formulae for the eigenvalues and the maxima of eigenfunctions are found, and comparison theorems are established. Bibliography: 20 titles.
Keywords: nonlinear eigenvalue problem, nonlinear problem of Sturm–Liouville type, eigenvalue asymptotics, comparison theorem, nonlinearizable solutions, integral characteristic equation. 
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D. V. Valovik; S. V. Tikhov. Existence of solutions of a~nonlinear eigenvalue problem and their properties. Sbornik. Mathematics, Tome 215 (2024) no. 1, pp. 52-73. http://geodesic.mathdoc.fr/item/SM_2024_215_1_a2/