Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain

Journal of Computational and Applied Mathematics

Volumn 113, Issue 1, 2000, Pages 365-380

  Erbe, Lynn ^a   Peterson, Allan ^a   Mathsen, Ronald ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b NORTH DAKOTA STATE UNIVERSITY   (United States)

Author keywords

Measure chains

Indexed keywords

MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; THEOREM PROVING;

BANACH SPACE;

BOUNDARY VALUE PROBLEMS;

EID: 0033883340     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00267-8     Document Type: Article

References (21)

1. R. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, preprint.
2. C. Ahlbrandt, A. Peterson, Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations, Kluwer Academic Publishers, Boston, 1996.
3. R. Agarwal, M. Bohner, Quadratic functionals for second order matrix equations on time scales, preprint.
4. R. Agarwal, M. Bohner, P. Wong, Sturm-Liouville eigenvalue problems on time scales, preprint.
5. B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, Non-linear Dynamics and Quantum Dynamical Systems, Akademie Verlag, Berlin, 1990.
6. W.A. Coppel, Disconjugacy, Lecture Notes in Mathematics, Springer, New York, 1971.
7. K. Deimling, Nonlinear Functional Analysis, Springer, New York, 1985.
8. L. Erbe, Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems, Math. Comput. Modelling, to appear.
9. L. Erbe, S. Hilger, Sturmian theory on measure chains, Differential Equations Dyn. Systems 1 (1993) 223-246.
10. L.H. Erbe, S. Hu, H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994) 640-648.
11. L.H. Erbe, A. Peterson, Green's functions and comparison theorems for differential equations on measure chains, Dyn. Continuous Discrete Impulsive Systems 6 (1999) 121-137.
12. L.H. Erbe, A. Peterson, Positive solutions for a nonlinear differential equation on a measure chain, Math. Comput. Modeling, to appear.
13. L.H. Erbe, A. Peterson, Eigenvalue conditions and positive solutions, J. Difference Equations Appl., to appear.
14. L.H. Erbe, M. Tang, Positive radial solutions to nonlinear boundary value problems for semilinear elliptic problems, in: Z. Deng et al. (Eds.), Differential Equations and Control Theory, Marcel Dekker, New York, 1995, pp. 45-53.
15. L.H. Erbe, M. Tang, Existence and Multiplicity of positive solutions to nonlinear boundary value problems, Differential Equations Dyn. Systems 4 (1996) 313-320.
16. J. Graef, C. Qian, B. Yang, Positive solutions to boundary value problems for nonlinear difference equations, J. Difference Equations, to appear.
17. S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18-56.
18. B. Kaymakcalan, V. Laksmikantham, S. Sivasundaram, Dynamical Systems on Measure Chains, Kluwer Academic Publishers, Boston, 1996.
19. W. Kelley, A. Peterson, Difference Equations: An Introduction with Applications, Academic Press, New York, 1991.
20. M. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
21. H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations 109 (1994) 1-7.