Nonlinear eigenvalue problems involving two classes of functional differential equations

Houston Journal of Mathematics

Volumn 26, Issue 3, 2000, Pages 597-608

  Davis, John M ^a   Prasad, K Rajendra ^b,c   Yin, William K C ^d  

^a BAYLOR UNIVERSITY   (United States)

^b AUBURN UNIVERSITY   (United States)

^c ANDHRA UNIVERSITY   (India)

^d LAGRANGE COLLEGE   (United States)

Author keywords

Boundary value problem; Functional differential equation; Nonlinear eigenvalue problem; Positive solution

Indexed keywords

EID: 0034366426     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. R.P. Agarwal and J. Henderson, Superlinear and sublinear focal boundary value problems, Appl. Anal. 60 (1996), 189-200.
2. R.P. Agarwal, D. O'Regan, and P.J.Y. Wong, "Positive Solutions of Differential, Difference and Integral Equations," Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
3. R.P. Agarwal and Q. Sheng, Right focal point boundary value problems for functional differential equations, in "Boundary Value Problems for Functional Differential Equations," World Scientific, Singapore, 1995.
4. D. Bainov and A. Domoshnitsky, Theorems on differential inequalities for second order functional differential equations, Glas. Mat. Ser. III 29 (1994), 275-289.
5. C. Bandle and M.K. Kwong, Semilinear elliptic problems in annular domains, Z. Angew. Math. Phys. 40 (1989), 245-257.
6. J.M. Davis, J. Henderson, K.R. Prasad, and W.K.C. Yin, Eigenvalue intervals for nonlinear right focal problems, Appl. Anal., 74 (2000), 215-231.
7. D.G. de Figueiredo, P.L. Lions, and R.D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl. 61 (1982), 41-63.
8. P.W. Eloe and J. Henderson, Inequalities based on a generalization of concavity, Proc. Amer. Math. Soc. 125 (1997), 2103-2107.
9. P.W. Eloe and J. Henderson, Singular nonlinear (k, n-k) conjugate boundary value problems, J. Differential Equations 133 (1997), 136-151.
10. L.H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743-748.
11. A. Friedman and B. McLeod, Optimal design of an optical lens, Arch. Rational Mech. Anal. 99 (1987), 147-164.
12. J.K. Hale and S.M. Verduyn Lunel, "Introduction to Functional Differential Equations," Springer-Verlag, New York, 1993.
13. J. Henderson and W.N. Hudson, Eigenvalue problems for nonlinear functional differential equations, Comm. Appl. Nonlinear Anal. 3 (1996), 51-58.
14. J. Henderson and W.K.C. Yin, Positive solutions and nonlinear eigenvalue problems for functional differential equations, Appl. Math. Lett. 12 (1999), 63-68.
15. S.G. Hu, Boundary value problems for functional differential equations involving eigenvalues, Acta Math. Appl. Sinica 20 (1997), 311-315.
16. D. Jiang and H. Liu, Existence of positive solutions to (k, n - k) conjugate boundary value problems, Kyushu J. Math. 53 (1998), 115-125.
17. M.A. Krasnosel'skii, "Positive Solutions of Operator Equations," Noordhoff, Groningen, 1964.
18. V.P. Maksimov and A.N. Rumyantsev, Constructive methods in the theory of functional differential equations and their computer aided implementation, Funct. Differ. Equ. 4 (1997), 133-141.
19. S.K. Ntouyas, Y.G. Sficas, and P.Ch. Tsamatos, Boundary value problems for functional differential equations, J. Math. Anal. Appl. 199 (1996), 213-220.
20. S.K. Ntouyas, Y.G. Sficas, and P.Ch. Tsamatos, An existence principle for boundary value problems for second order functional differential equations, Nonlinear Anal. 20 (1993), 215-222.
21. D. Taunton and W.K.C. Yin, Existence of solutions of some functional differential equations, Comm. Appl. Nonlinear Anal. 4 (1997), 31-43.
22. B. van-Brunt and J.R. Ockendon, A lens focusing light at two different wavelengths, J. Math. Anal. Appl. 165 (1992), 156-179.