Abstract
We introduce the concept of weighted sequence space \(bv_p^\omega \) and we construct a Hausdorff measure of noncompactness (MNC) in this space. Then, by applying this MNC we study the existence of solutions of infinite systems of third-order three-point nonhomogeneous boundary value problem in \(bv_p^{\omega }\). Finally, we present two examples to show the usefulness of our results.
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Aghajani, A., Banaś, J., Jalilian, Y.: Existence of solution for a class of nonlinear Volterra singular integral equation. Comput. Math. Appl. 62, 1215–1227 (2011)
Aghajani, A., Mursaleen, M., Shole Haghighi, A.: Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness. Acta Math. Sci. 35B, 552–566 (2015)
Aghajani, A., Pourhadi, E.: Application of measure of noncompactness to \(l_1\)-solvability of infinite systems of second order differential equations. Bull. Belg. Math. Soc. Simon Stevin 22(1), 105–118 (2015)
Alotaibi, A., Mursaleen, M., Alamri, B.A.S.: Solvability of second order linear differential equations in the sequence space \(n(\phi )\). Adv. Differ. Equ. 2018, 377 (2018)
Anderson, D.: Green’s function for a third-order generalized right focal problem. J. Math. Anal. Appl. 288, 1–14 (2003)
Anderson, D.: Multiple positive solutions for a three-point boundary value problem. Math. Comput. Model. 27, 49–57 (1998)
Anderson, D., Davis, J.M.: Multiple solutions and eigenvalues for third-order right focal boundary value problems. J. Math. Anal. Appl. 267, 135–157 (2002)
Bai, Z., Fei, X.: Existence of triple positive solutions for a third order generalized right focal problem. Math. Inequal. Appl. 9, 437–444 (2006)
Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60. Marcel Dekker, New York (1980)
Banaś, J., Lecko, M.: Solvability of infinite systems of differential equations in Banach sequence spaces. J. Comput. Appl. Math. 137, 363–375 (2001)
Banaś, J., Mursaleen, M.: Sequence Spaces and Measure of Noncompactness with Applications to Differential and Integral Equation. Springer, New Delhi (2014)
Banaś, J., Mursaleen, M., Rizvi, S.M.H.: Existence of solutions to a boundary-value problem for an infinite system of differential equations. Electron. J. Differ. Equ. 262, 12 (2017)
Basar, F.: Summability Theory and its Appliactions. Bentham Science Publishers, Sharjah (2011)
Basar, F., Altay, B.: On the space of sequences of \(p-\)bounded variation and related matrix mappings. Ukr. Math. J. 55, 136–147 (2003)
Bellman, R.: Methods of Nonlinear Analysis, vol. II. Academic Press, New York (1973)
Boucherif, A., Al-Malki, N.: Nonlinear three-point third order boundary value problems. Appl. Math. Comput. 190, 1168–1177 (2007)
Deimling, K.: Ordinary Differential Equations in Banach Spaces. Lecture Notes in Mathematics, vol. 596. Springer, Berlin (1977)
Graef, J.R., Yang, B.: Multiple positive solutions to a three point third order boundary value problem. Discrete Contin. Dyn. Syst. (Suppl.), 1–8 (2005)
Gregus, M.: Third Order Linear Differential Equations. Mathematics and its Applications, Reidel, Dordrecht (1987)
Grossinho, M.R., Minhos, F.M.: Existence result for some third order separated boundary value problems. Nonlinear Anal. 47, 2407–2418 (2001)
Hazarika, B., Das, A., Arab, R., Mursaleen, M.: Solvability of the infinite system of integral equations in two variables in the sequence spaces \(c_0\) and \(l_1\). J. Comput. Appl. Math. 326, 183–192 (2012)
Jarrah, A.M., Malkowsky, E.: Ordinary, absolute and strong summability and matrix transformations. Filomat 17, 59–78 (2003)
Kuratowski, K.: Sur les espaces complets. Fund. Math. 15, 301–309 (1930)
Meir, A., Keeler, E.A.: Theorem on contraction mappings. J. Math. Anal. Appl. 28, 326–329 (1969)
Mursaleen, M.: Application of measure of noncompactness to infinite system of differential equations. Canad. Math. Bull. 56, 388–394 (2013)
Mursaleen, M.: Some geometric properties of a sequence space related to \(l_p\). Bull. Aust. Math. Soc. 67(2), 343–347 (2003)
Mursaleen, M., Bilalov, B., Rizvi, S.M.H.: Applications of measures of noncompactness to infinite system of fractional differential equations. Filomat 31(11), 3421–3432 (2017)
Mursaleen, M., Mohiuddine, S.A.: Applications of measures of noncompactness to the infinite system of differential equations in \(l_p\) spaces. Nonlinear Anal. 75, 2111–2115 (2012)
Mursaleen, M., Rizvi, S.M.H.: Solvability of infinite system of second order differential equations in \(c_0\) and \(l_1\) by Meir-Keeler condensing operator. Proc. Am. Math. Soc. 144(10), 4279–4289 (2016)
Oguzt Poreli, M.N.: On the neural equations of Cowan and Stein. Util. Math. 2, 305–315 (1972)
Pouhadi, E., Mursaleen, M., R, S.: On a class of infinite system of third-order differential equations in \(l_{p}\) via measure of noncompactness. Filomat 34(11), 3861–3870 (2020)
Saadati, R., Pourhadi, E., Mursaleen, M.: Solvability of infinite systems of third-order differential equations in \(c_0\) by Meir-Keeler condensing operators. J. Fixed Point Theory Appl. 21(2), 1–16 (2019)
Sun, Y.: Positive solutions for third-order three-point nonhomogeneous boundary value problems. Appl. Math. Lett. 22, 45–51 (2009)
Sun, Y.: Positive solutions of singular third-order three-point boundary value problems. J. Math. Anal. Appl. 306, 589–603 (2005)
Yao, Q.: The existence and multiplicity of positive solutions for a third-order three-point boundary value problem. Acta Math. Appl. Sin. 19, 117–122 (2003)
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Amiri Kayvanloo, H., Khanehgir, M. & Mursaleen, M. Solution of infinite system of third-order three-point nonhomogeneous boundary value problem in weighted sequence space \({{\varvec{bv}}}_{{{\varvec{p}}}}^{\omega }\). Rend. Circ. Mat. Palermo, II. Ser 73, 1329–1342 (2024). https://doi.org/10.1007/s12215-023-00986-1
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DOI: https://doi.org/10.1007/s12215-023-00986-1