scholarly journals On the reduction of a nonlinear Noetherian differential-algebraic boundary-value problem to a noncritical case

2019 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Nonlinear Oscillations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Differential Algebraic Equations ◽  
Nonlinear Boundary Value Problems ◽  
Actual Problem ◽  
Nonlinear Boundary Value

The study of the differential-algebraic boundary value problems was established in the papers of K. Weierstrass, M.M. Lusin and F.R. Gantmacher. Works of S. Campbell, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, M.O. Perestyuk, V.P. Yakovets, O.A. Boichuk, A. Ilchmann and T. Reis are devoted to the systematic study of differential-algebraic boundary value problems. At the same time, the study of differential-algebraic boundary-value problems is closely related to the study of nonlinear boundary-value problems for ordinary differential equations, initiated in the works of A. Poincare, A.M. Lyapunov, M.M. Krylov, N.N. Bogolyubov, I.G. Malkin, A.D. Myshkis, E.A. Grebenikov, Yu.A. Ryabov, Yu.A. Mitropolsky, I.T. Kiguradze, A.M. Samoilenko, M.O. Perestyuk and O.A. Boichuk. The study of the nonlinear differential-algebraic boundary value problems is connected with numerous applications of corresponding mathematical models in the theory of nonlinear oscillations, mechanics, biology, radio engineering, the theory of the motion stability. Thus, the actual problem is the transfer of the results obtained in the articles and monographs of S. Campbell, A.M. Samoilenko and O.A. Boichuk on the nonlinear boundary value problems for the differential algebraic equations, in particular, finding the necessary and sufficient conditions of the existence of the desired solutions of the nonlinear differential algebraic boundary value problems. In this article we found the conditions of the existence and constructed the iterative scheme for finding the solutions of the weakly nonlinear Noetherian differential-algebraic boundary value problem. The proposed scheme of the research of the nonlinear differential-algebraic boundary value problems in the article can be transferred to the nonlinear matrix differential-algebraic boundary value problems. On the other hand, the proposed scheme of the research of the nonlinear Noetherian differential-algebraic boundary value problems in the critical case in this article can be transferred to the autonomous seminonlinear differential-algebraic boundary value problems.

scholarly journals On Nonlinear Boundary Value Problems for Functional Difference Equations withp-Laplacian

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Yong Wan ◽  
Yuji Liu
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Functional Difference ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Functional Difference Equations

Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations withp-Laplacian are established by making of continuation theorems. We allowfto be at most linear, superlinear, or sublinear in obtained results.

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