Existence of solutions to the nonlinear,singular second order Bohr boundary value problems |
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| Institution: | 1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, PR China;2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China;3. School of Science, Xi’an Polytechnic University, Xi’an, 710048, PR China;1. Dpto. de Matemática Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain;2. Dpto. de Estadística e Investigación Operativa, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain;1. Faculdade de Matemática, Universidade Federal do Pará, 66075-110, Belém - PA, Brazil;2. Departamento de Matemática, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, SP, Brazil;1. Dipartimento di Matematica, Università deli Studi di Roma Sapienza, P.le Aldo Moro 5, 00185 Roma, Italy;2. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy;1. Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, PR China;2. Department of Mathematics, Nanjing University, Nanjing, 210093, PR China;3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, PR China |
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| Abstract: | This paper investigates the existence of solutions for nonlinear systems of second order, singular boundary value problems (BVPs) with Bohr boundary conditions. A key application that arises from this theory is the famous Thomas–Fermi equations for the model of the atom when it is in a neutral state. The methodology in this paper uses an alternative and equivalent BVP, which is in the class of resonant singular BVPs, and thus this paper obtains novel results by implementing an innovative differential inequality, Lyapunov functions and topological techniques. This approach furnishes new results in the area of singular BVPs for a priori bounds and existence of solutions, where the BVP has unrestricted growth conditions and subject to the Bohr boundary conditions. In addition, the results can be relaxed and hold for the non-singular case too. |
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| Keywords: | Boundary value problem Singular Resonant BVPs Existence of solutions Thomas–Fermi Bohr |
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