Monotone method for the Neumann problem with lower and upper solutions in the reverse order

Applied Mathematics and Computation

Volumn 117, Issue 1, 2001, Pages 1-14

  Cabada, Alberto ^a   Habets, Patrick ^b   Lois, Susana ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b Inst Mathematiques Pures et Appl   (Belgium)

Author keywords

Anti maximum principles; Nonlinear boundary value problem

Indexed keywords

EID: 0346941595     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(99)00149-6     Document Type: Article

References (12)

1. A. Amann, A. Ambrosetti, G. Mancini, Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z. 158 (1978) 179-194.
2. B.N. Babkin, Solution of a boundary value problem for an ordinary differential equation of second order by Chaplygin's method, Prikl. Mat. Mekh. 18 (1954) 239-242.
3. A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl. 185 (1994) 302-320.
4. A. Cabada, L. Sanchez, A positive operator approach to the Neumann problem for a second order ordinary differential equation, J. Math. Anal. Appl. 204 (1996) 774-785.
5. C. De Coster, P. Habets, Upper and lower solutions in the theory of ODE boundary value problems: classical and recent results, in: F. Zanolin (Ed.), Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, C.I.S.M. Courses and Lectures 371, Springer, New York, 1996, pp. 1-79.
6. C. De Coster, M. Henrard, Existence and localization of solution for elliptic problem in presence of lower and upper solutions without any order, J. Differential Equations 145 (1998) 420-452.
7. Gendzhoyan, On two-sided Chaplygin approximations to the solution of the two point boundary value problem, Izv. SSR Jiz. Mate. Nauk. 17 (1964) 21-27.
8. P. Omari, A monotone method for constructing extremal solutions of second order scalar boundary value problems, Appl. Math. Comput 18 (1986) 257-275.
9. E. Picard, Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires, J. Math. 9 (1893) 217-271.
10. G. Scorza Dragoni, II problema dei valori ai limiti studiato in grande per le equazioni differenziali del secondo ordine, Math. Ann. 105 (1931) 133-143.
11. G. Scorza Dragoni, Intorno a un criterio di esistenza per un problema di valori ai limiti, Rend. Semin. R. Accad. Naz. Lincei 28 (1938) 317-325.
12. M.X. Wang, A. Cabada, J.J. Nieto, Monotone method for nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 58 (1993) 221-235.