On the existence of solutions of boundary value problems for second order differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 32, Issue 4, 1998, Pages 563-573

  Kelevedjiev, Petio ^a  

^a TECHNICAL UNIVERSITY OF SOFIA   (Bulgaria)

Author keywords

A priori bounds; Barrier strips; Boundary value problems; Existence; Local continuity; Topological transversality theorem

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING; TOPOLOGY;

SECOND ORDER DIFFERENTIAL EQUATIONS; TOPOLOGICAL TRANSVERSALITY THEOREM;

BOUNDARY VALUE PROBLEMS;

EID: 0032058498     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0362-546x(97)00487-2     Document Type: Article

References (17)

1. Bailey, P. B., Shampine, L. F. and Waltman, P. E., Nonlinear Two-point Boundary Value Problems. Academic Press, New York, 1968.
2. Baxley, J. and Brown, S., Existence and uniqueness for two-point boundary value problems. Proc. Roy. Soc. Edinburgh, 1981, 88A, 219-234.
3. Bebernes, J. and Gaines, R., Dependence on boundary data and a generalized boundary value problem. J. Diff. Eqns, 1968, 4, 359-368.
4. Bernfeld, S. R. and Lakshmikantham, V., An Introduction to Nonlinear Boundary Value Problems. Academic Press, New York, 1974.
5. Erbe, L. H., Existence of solutions to boundary value problems for second-order differential equations. Nonlinear Analysis, 1982, 6, 1155-1162.
6. Granas, R.E., Guenther, R. B. and Lee, J. W., Nonlinear boundary value problems for ordinary differential equations. Dissnes Math., 1985, 244, 1-128.
7. Mawhin, J. and Schmitt, K., Upper and lower solutions and semilinear second order elliptic equations with non-linear boundary conditions. Proc. Roy. Soc. Edinburgh, 1984, 97A, 199-207.
8. Bobisud, L. E., O'Regan, D. and Royalty, W. D., Solvability of some nonlinear boundary value problems. Nonlinear Analysis, 1988, 12, 855-869.
9. Tineo, A., Existence theorem for a singular two-point Dirichlet problem. Nonlinear Analysis, 1992, 19, 323-333.
10. O'Regan, D., Existence of positive solutions to some singular and nonsingular second order boundary value problems. J. Diff. Eqns, 1990, 84, 228-251.
11. O'Regan, D., Theory of Singular Boundary Value Problems. World Scientific, 1994.
12. Gudkov, V. V., Klokov, I. A., Lepin, A. Y. and Ponomarev, V. D., Two-point Boundary Value Problems for Ordinary Differential Equations. Izdat. "Zinatnoe", Riga, 1973 (in Russian).
13. Guennoun Zine, E. A., Existence de solutions on sens de Carateodory pour le probleme de Neuman y″ = f(t,y,y′). Canad. J. Math., 1991, 43, 998-1009.
14. Jackson, L. K. and Palamides, P. K., An existence theorem for a nonlinear two-point boundary value problem. J. Diff. Eqns, 1984, 53, 48-66.
15. Kelevedjiev, P., Existence of solutions for two-point boundary value problems. Nonlinear Analysis, 1994, 22, 217-224.
16. Kelevedjiev, P., Solvability of two point boundary value problems. Nonlinear Analysis, 1996, 27, 309.
17. Granas, A., Guenther, R. B. and Lee, J. W., Topological transversality - II. Applications to the Neumann problem to y″ = f(t,y,y′). Pacif. J. Math., 1983, 104, 95-109.