Solvability of the infinite systems of nonlinear third-order differential equations in the weighted sequence space ${\bf m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}, \psi,q)}$
Subject Areas : Fixed point theoryM. Khanehgir 1 , H. Amiri Kayvanloo 2 , R. Allahyari 3 , M. Mehrabinezhad 4
1 - Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran
3 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
4 - Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran
Keywords:
Abstract :
[1] A. Aghajani, J. Banas, Y. Jalilian, Existence of solution for a class of nonlinear Volterra singular integral equation, Comput. Math. Appl. 62 (2011), 1215-1227.
[2] A. Aghajani, M. Mursaleen, A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta. Math. Sci. 35B (2015), 552-566.
[3] A. Aghajani, N. Sabzali, Existence of coupled fixed points via measure of noncompactness and applications, J. Nonlinear Convex Anal. 15 (2014), 941-952.
[4] J. Banas, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, 60 Marcel Dekker, New York, 1980.
[5] J. Banas, M. Mursaleen, Sequence Spaces and Measure of Noncompactness with Applications to Differential and Integral Equation, Springer, India, 2014.
[6] A. Bhrawy, W. Abd-Elhameed, New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method, Math. Probl. Eng. Art. (2011), 2011:837218.
[7] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lecture Notes in Mathematics, Springer, Berlin, 1977.
[8] Z. Du, B. Zhao, Z. Bai, Solvability of a third-order multipoint boundary value problem at resonance, Abstr. Appl. Anal. (2014), 2014:931217.
[9] X. Feng, H. Feng, D. Bai, Eigenvalue for a singular third-order three-point boundary value problem, Appl. Math. Comput. 219 (2013), 9783-9790.
[10] Y. Feng, S. Liu, Solvability of a third-order two-point boundray value problem, Appl. Math. Lett. 18 (2005), 1034-1040.
[11] A. Ghanenia, M. Khanehgir, M. Mehrabinezhad, R. Allahyari, H. Amiri Kayvanloo, Solvability of infinite systems of second order differential equations in the sequence space, Rend. Circ. Mat. Palermo, II. Ser. 69 (2020), 1-11.
[12] J. Graef, B. Yang, Positive solutions of a nonlinear third order eigenvalue problem, Dyn. Syst. Appl. 15 (2006), 97-110.
[13] M. Gregus, Third Order Linear Differential Equations, in: Math. Appl., Reidel, Dordrecht, 1987.
[14] L. Guo, L. J. Sun, Y. Zhao, Existence of positive solutions for nonlinear third-order three-point boundary
value problems, Nonlinear Anal. 68 (2008), 3151-3158.
[15] B. Hazarika, A. Das, R. Arab, M. Mursaleen, Solvability of the infinite system of integral equations in two variables in the sequence spaces c0and l1, J. Comput. Appl. Math. 326 (2012), 183-192.
[16] K. Kuratowski, Sur les espaces complets, Fund Math. 15 (1930), 301-309.
[17] Y. Li, Y. Guo, G. Li, Existence of positive solutions for systems of nonlinear third-order differential equations, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 3792-3797.
[18] X. Lin, Z. Zhao, Iterative technique for a third-order differential equation with three-point nonlinear boundary value conditions, Elect. J. Qual. Theory. Diff. Equ. (2016), 2016:1-10.
[19] A. Meir, E. A. Keeler, Theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
[20] M. Mursaleen, Application of measure of noncompactness to infinite system of differential equations, Can. Math. Bull. 56 (2013), 388-394.
[21] M. Mursaleen, Some geometric properties of a sequence space related to lp, Bull. Aust. Math. Soc. 67 (2003), 343-347.
[22] M. Mursaleen, B. Bilalov, S. M. H. Rizvi, Applications of measures of noncompactness to infinite system of fractional differential equations, Filomat. 31 (2017), 3421-3432.
[23] M. N. Oguzt Poreli, On the neural equations of Cowan and Stein, Utilitas Math. 2 (1972), 305-315.
[24] N. Sapkota, R. Das, Application of measure of non-compactness for the existence of solutions of an infinite system of differential equations in the sequence spaces of convergent and bounded series, Adv. Intell. Syst. Comput. 1262 (2021), 167-177.
[25] A. Vakeel, A. Khan, New type of difference sequence spaces, Applied Sci. 12 (2010), 102-108.