Geodesic
Nonlinear impulsive Hahn — Sturm — Liouville problems on the whole line
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 4, pp. 500-519
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Impulsive Hahn — Sturm — Liouville problems in singular cases are discussed. The existence of solutions of such equations on the whole axis and in the case of Weyl's limit-circle has been investigated. First, we construct the corresponding Green's function. This boundary-value problem is thus reduced to a fixed point problem. Later, we demonstrate the existence and uniqueness of the solutions to this problem by using the traditional Banach fixed point theorem. Finally, we derive an existence theorem without considering the solution's uniqueness. We apply the well-known Schauder fixed point to obtain this result.
Keywords: Hahn difference equations, singular nonlinear problems, boundary-value problems with impulses. 
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     author = {B. P. Allahverdiev and H. Tuna and H. A. Isayev},
     title = {Nonlinear impulsive {Hahn} {\textemdash} {Sturm} {\textemdash} {Liouville} problems on the whole line},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {500--519},
     year = {2024},
     volume = {20},
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B. P. Allahverdiev; H. Tuna; H. A. Isayev. Nonlinear impulsive Hahn — Sturm — Liouville problems on the whole line. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 4, pp. 500-519. http://geodesic.mathdoc.fr/item/VSPUI_2024_20_4_a5/

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