Geodesic
On the existence and uniqueness of a solution to the boundary value problem for linear ordinary differential equations
Nizami A. Gasilov1 ; Nizami A. Gasilov
1Department of Computer Engineering, Baskent University, Ankara, Turkey
Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 4, pp. 205-224 
Nizami A. Gasilov; Nizami A. Gasilov. On the existence and uniqueness of a solution to the boundary value problem for linear ordinary differential equations. Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 4, pp. 205-224. http://geodesic.mathdoc.fr/item/AMUC_2024_93_4_a2/
@article{AMUC_2024_93_4_a2,
     author = {Nizami A. Gasilov and Nizami A. Gasilov},
     title = { On the existence and uniqueness of a solution to the boundary value problem for linear ordinary differential equations},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {205--224},
     year = {2024},
     volume = {93},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2024_93_4_a2/}
}
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In this study, we investigate the Boundary Value Problem (BVP) for second order non-homogeneous linear differential equation with Dirichlet conditions. We derive a novel sufficient condition for the existence and uniqueness of a solution. The condition is formulated in terms of input parameters (coefficient functions and the length $l$ of the interval, where the BVP is considered), not in secondary terms as Lipschitz coefficients. We compare the obtained sufficient condition with those for non-linear BVPs and demonstrate that it covers a significantly wider class of BVPs.