A monotone iterative method for second order nonlinear problems with boundary conditions driven by maximal monotone multivalued operators
Authors
D. A. Béhi
- Université de Man, BP 20 Man, Côte d'Ivoire.
Abstract
In this paper, we study the following second order differential equation: \(-\left(\Phi(u'(t)) \right) '+\phi_p(u(t)) = \varepsilon f(t,u(t)) \text{ a.e. on }\Omega = [0, T]\) under nonlinear multivalued boundary value conditions which incorporate as special cases the classicals boundary value conditions of type Dirichlet, Neumann, and Sturm-Liouville. Using monotone iterative method coupled with lower and upper solutions method, multifunction analysis, theory of monotone operators, and theory of topological degree, we show existence of solution and extremal solutions when the lower and upper solutions are well ordered or not. Since the boundary value conditions do not include the periodic one, we show that our method stay true for the periodic problem.
Share and Cite
ISRP Style
D. A. Béhi, A monotone iterative method for second order nonlinear problems with boundary conditions driven by maximal monotone multivalued operators, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 1, 1--18
AMA Style
Béhi D. A., A monotone iterative method for second order nonlinear problems with boundary conditions driven by maximal monotone multivalued operators. J. Nonlinear Sci. Appl. (2024); 17(1):1--18
Chicago/Turabian Style
Béhi, D. A.. "A monotone iterative method for second order nonlinear problems with boundary conditions driven by maximal monotone multivalued operators." Journal of Nonlinear Sciences and Applications, 17, no. 1 (2024): 1--18
Keywords
- \( \Phi\)-Laplacian
- lower and upper solutions
- monotone iterative method
- Carathéodory function
- maximal monotone multivalued operators
- Leray-Schauder's degree
- extremal solutions
MSC
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