Existence of a solution of a three-point boundary value problem and the spectral radius of a related linear operator

Nonlinear Analysis, Theory, Methods and Applications

Volumn 34, Issue 4, 1998, Pages 489-507

  Gupta, Chaitan P ^a   Trofimchuk, Sergej I ^b  

^a UNIVERSITY OF NEVADA   (United States)

^b INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

Caratheodory's conditions; Comparison results; Initial value problem; Leray Schauder Continuation theorem; Spectral radius; Three point boundary value problem

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

CARATHEODORY'S CONDITIONS; LERAY SCHAUDER CONTINUATION THEOREM; THREE-POINT BOUNDARY VALUE PROBLEM;

INITIAL VALUE PROBLEMS;

EID: 0032210464     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00584-1     Document Type: Article

References (19)

1. V.A. Il'in, E.I. Moiseev, Non-local boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differential Equations 23 (7) (1987) 803-810.
2. V.A. Il'in, E. I. Moiseev, Non-local boundary value problem of the second kind for a Sturm-Liouville operator, Differential Equations 23 (8) (1987) 979-987.
3. A.V. Bitsadze, On the theory of non-local boundary value problems, Soviet Math. Dokl. 30 (1) (1984) 8-10.
4. A.V. Bitsadze, On a class of conditionally solvable non-local boundary value problems for harmonic functions, Soviet Math. Dokl. 31 (1) (1985) 91-94.
5. A.V. Bitsadze, A.A. Samarskii, On some simple generalizations of linear elliptic boundary problems, Soviet Math. Dokl. 10 (2) (1969) 398-400.
6. C.P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Analysis 24 (1995) 1483-1489.
7. C.P. Gupta, Solvability of a multi-point boundary value problem at resonance, Results in Math. 28 (1995) 270-276.
8. C.P. Gupta, Existence theorems for a second order m-point boundary value problem at resonance, Int. J. Math. & Math. Sci. 18 (1995) 705-710.
9. C.P. Gupta, S.K. Ntouyas, P.Ch. Tsamatos, On an m-point boundary value problem for second order ordinary differential equations, Nonlinear Analysis 23 (1994) 1427-1436.
10. C.P. Gupta, S.K. Ntouyas, P.Ch. Tsamatos, Existence results for m-point boundary value problems, Diff. Equations and Dynamical Systems 2 (1994) 289-298.
11. C.P. Gupta, S.K. Ntouyas, P.Ch. Tsamatos, Solvability of an m-point boundary value problem for second order ordinary differential equations, J. Math. Anal. & Appl. 189 (1995) 575-584.
12. A.A. Martynyuk, V. Lakshmikantham, S. Leela, Motion Stability: the Method of Integral Inequalities (in Russian).
13. N. Dunford, J.T. Schwartz, Linear Operators, vol. 1, Interscience Publishers, New York, 1958.
14. K. Yosida, Functional Analysis, Springer, Berlin, 1965.
15. C.P. Gupta, A note on a second order three-point boundary value problem, J. Math. Anal. & Appl. 186 (1994) 277-281.
16. A.F. Filippov, Differential Equations with Discontinuous Right-hand Sides, Kluwer Academic Publishers, Boston, MA, 1988.
17. V. Lakshmikantham, S. Leela, A.A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York, 1989.
18. C.P. Gupta, S.I. Trofimchuk, A sharper condition for the solvability of a three-point second order boundary value problem, J. Math. Anal. and Appl. 205 (1997) 586-597.
19. C.P. Gupta, S.I. Trofimchuk, Solvability of a multi-point boundary value problem and related a priori estimates, Canadian Applied Mathematics Quarterly, to appear.