Optimal constants in a nonlocal boundary value problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 5-7, 2005, Pages 672-685

  Webb, J R L ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Optimal constants; Positive solutions; Principal eigenvalue; Thermostat model

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; THERMOSTATS;

OPTIMAL CONSTANTS; POSITIVE SOLUTIONS; PRINCIPAL EIGENVALUE; THERMOSTAT MODELS;

BOUNDARY VALUE PROBLEMS;

EID: 28044436735     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.02.055     Document Type: Conference Paper

References (16)

1. H. Amann Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces SIAM. Rev. 18 1976 620 709
2. L. Erbe Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems Math. Comput. Modelling 32 2000 529 539
3. P. Guidotti, and S. Merino Gradual loss of positivity and hidden invariant cones in a scalar heat equation Differential Integral Equations 13 2000 1551 1568
4. D. Guo, and V. Lakshmikantham Nonlinear Problems in Abstract Cones 1988 Academic Press New York
5. C.P. Gupta, S.K. Ntouyas, and P.Ch. Tsamatos On an m-point boundary-value problem for second-order ordinary differential equations Nonlinear Anal. 23 1994 1427 1436
6. C.P. Gupta, S.K. Ntouyas, and 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
7. G. Infante, J.R.L. Webb, Loss of positivity in a nonlinear scalar heat equation, Nonlinear Differential Equations Appl., to appear.
8. G. Infante, J.R.L. Webb, Nontrivial solutions of perturbed Hammerstein integral equations, submitted.
9. K.Q. Lan Multiple positive solutions of semilinear differential equations with singularities J. London Math. Soc. 63 2 2001 690 704
10. K.Q. Lan, and J.R.L. Webb Positive solutions of semilinear differential equations with singularities J. Differential Equations 148 1998 407 421
11. R. Ma Positive solutions of a nonlinear m-point boundary value problem Comput. Math. Appl. 42 2001 755 765
12. R.H. Martin Nonlinear Operators and Differential Equations in Banach Spaces 1976 Wiley New York
13. R.D. Nussbaum, Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem, in: E. Fadell, G. Fournier (Eds.), Fixed Point Theory, Lecture Notes in Mathematics, vol. 886, Springer, Berlin, 1981, pp. 309-330.
14. J.R.L. Webb, Remarks on positive solutions of three point boundary value problems, Dynamical systems and differential equations (Wilmington, NC, 2002), Discrete Contin. Dynam. Systems 2003, Added Volume, pp. 905-915.
15. J.R.L. Webb, Eigenvalue criteria for a heat flow problem, Discrete Contin. Dynam. Systems, to appear.
16. J.R.L. Webb, K.Q. Lan, Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type, submitted.