Positive solutions for a coupled system of non linear of second-order boundary-valued differential equations
Abstract
The main objective of this article is concerned with existence and uniqueness of the positive solutions for a coupled system of second-order boundary-valued differential equations, which the boundary conditions are coupled by integrals. For that one, the solutions are related to Green’s functions and represented by integral equations and so that, we used a cone compression and expansion fixed point theorem applied to a completely continuous operator, as seen in Guo, D. and Lakshmikant V (1988).
Downloads
References
Asif, N. A., y Khan, R. A. (2012). Positive solutions to singular system withfour-point coupled boundary conditions. Journal of Mathematical Analysis and Applications, 386(2), 848-861.
Asif, N. A., Khan, R. A., y Henderson, J. (2010). Existence of positive solutions to a system of singular boundary value problems. Dynamic Systems and Applications, 19(2), 395-404.
Botelho, G., Pellegrino, D. y Teixeira, E. (2015). Fundamentos del análisis funcional. SBM. Cheng, X., y Zhong, C. (2005). Existence of positive solutions for a second-order ordinary differential system. Journal of Mathematical Analysis and Applications,312(1), 14-23.
Cui, Y., Liu, L., y Zhang, X. (2013). Uniqueness and existence of positive solutions for singular differential systems with coupled integral boundary value problems. In Abstract and Applied Analysis (Vol. 2013). Hindawi Publishing Corporation.
Cortez,M. , Quique, J.(2023)Existência de solução de um sistema acoplado elíptico não-linear
Brazilian Journal of Development, Curitiba, v.9, n.7, p. 22161-22171
Cassius Vinícius Casaro, Diego Márcio Gonzaga, Marco Rogério da Silva Richetto, Kátia Celina da Silva Richetto.(2022) Implementação de automatização do processo de fabricação de polímero utilizando a plataforma SDCD YokogawaCentum VP, BrazilianJournalofdevelopment Vol. 8 No. 12.
Cui, Y., y Sun, J. (2012). On existence of positive solutions of coupled integral boundary value problems for a nonlinear singular superlinear differential system.Electronic Journal of Qualitative Theory of Differential Equations, 2012(41), 1- 13.
Cui, Y., y Zou, Y. (2015).An existence and uniqueness theorem for a second order nonlinear system with coupled integral boundary value conditions. Applied Mathematics and computation, 2015(256), 438- 444.
Dajun,G. and Lakshmikanthan,V.(1988), Nonlinear problems in abstract cones, Academic Press, Inc.N.Y.
Doering, C. y Lopes A. (2016). Equaçõesdiferenciaisordinárias. Instituto de matemática pura e aplicada-IMPA. (6ª Ed.). IMPA, Rio de Janeiro, Brasil. 423 p.
Dugundji, J.(1951) An extension of Tietze's Theorem, Pacific J. Math., 1, 353-367.
Liu, B., Liu, L., y Wu, Y. (2008). Positive solutions for a singular second-order threepoint boundary value problem. Applied Mathematics and Computation, 196(2), 532- 541.
Lu¨, H., Yu, H., y Liu, Y. (2005). Positive solutions for singular boundary value problems of a coupled system of differential equations. Journal of MathematicalAnalysis and Applications, 302(1), 14-29
The authors and co-authors warrant that the article is their original work, does not infringe any copyright, and has not been published elsewhere. By submitting the article to GPH - International Journal of Mathematics, the authors agree that the journal has the right to retract or remove the article in case of proven ethical misconduct.
