Uniqueness and nonexistence of positive solutions to semipositone problems

Bulletin of the London Mathematical Society

Volumn 38, Issue 6, 2006, Pages 1033-1044

  Dancer, E Norman ^a   Shi, Junping ^b,c  

^a UNIVERSITY OF SYDNEY   (Australia)

^b The College of William and Mary   (United States)

^c HARBIN NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845724782     PISSN: 00246093     EISSN: 14692120     Source Type: Journal    
DOI: 10.1112/S0024609306018984     Document Type: Article

References (24)

1. W. ALLEGRETTO, P. NISTRI and P. ZECCA, 'Positive solutions of elliptic nonpositone problems', Differential Integral Equations 5 (1992) 95-101.
2. A. AMBROSETTI, D. ARCOYA and B. BUFFONI, 'Positive solutions for some semi-positone problems via bifurcation theory', Differential Integral Equations 7 (1994) 655-663.
3. S. B. ANGENENT, 'Uniqueness of the solution of a semilinear boundary value problem', Math. Ann. 272 (1985) 129-138.
4. I. J. BAKELMAN, Convex analysis and nonlinear geometric elliptic equations (Springer, Berlin, 1994).
5. H. BERESTYCKI, L. CAFFARELLI and L. NIRENBERG, 'Further qualitative properties for elliptic equations in unbounded domains', Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 69-94.
6. K. J. BROWN, A. CASTRO and R. SHIVAJI, 'Nonexistence of radially symmetric nonnegative solutions for a class of semi-positone problems', Differential Integral Equations 2 (1989) 541-545.
7. A. CASTRO, M. Hassanpour and R. Shivaji, 'Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearity', Comm. Partial Differential Equations 20 (1995) 1927-1936.
8. A. CASTRO and R. SHIVAJI, 'Nonnegative solutions for a class of radially symmetric nonpositone problems', Proc. Amer. Math. Soc. 106 (1989) 735-740.
9. A. CASTRO and G. SUDHASREE, 'Uniqueness of stable and unstable positive solutions for semipositone problems', Nonlinear Anal. 22 (1994) 425-429.
10. P. CLÉMENT and G. SWEERS, 'Existence and multiplicity results for a semilinear elliptic eigenvalue problem', Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987) 97-121.
11. E. N. DANCER, 'On the number of positive solutions of weakly nonlinear elliptic equations when a parameter is large', Proc. London Math. Soc. (3) 53 (1986) 429-452.
12. E. N. DANCER, 'Some notes on the method of moving planes', Bull. Austral. Math. Soc. 46 (1992) 425-434.
13. n or on bounded domains with small diffusion', Trans. Amer. Math. Soc. 357 (2005) 1225-1243.
14. n or on bounded domains with small diffusion. II', Indiana Univ. Math. J. 53 (2004) 97-108.
15. E. N. DANCER, 'Weakly nonlinear Dirichlet problems on long or thin domains', Mem. Amer. Math. Soc. 105 (1993) 1-66.
16. E. N. DANCER and K. SCHMITT, 'On positive solutions of semilinear elliptic equations', Proc. Amer. Math. Soc. 101 (1987) 445-452.
17. 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. (9) 61 (1982) 41-63.
18. B. GIDAS, W. M. NI and L. NIRENBERG, 'Symmetry and related properties via the maximum principle', Comm. Math. Phys. 68 (1979) 209-243.
19. D. GILBARG and N. S. TRUDINGER, Elliptic partial differential equations of second order, 2nd edn (Springer, Berlin/New York, 1983).
20. S. ORUGANTI, J. SHI and R. SHIVAJI, 'Diffusive logistic equation with constant effort harvesting, I: Steady states', Trans. Amer. Math. Soc. 354 (2002) 3601-3619.
21. T. OUYANG and J. SHI, 'Exact multiplicity of positive solutions for a class of semilinear problem', J. Differential Equations 146 (1998) 121-156.
22. T. OUYANG and J. SHI, 'Exact multiplicity of positive solutions for a class of semilinear problem: II', J. Differential Equations 158 (1999) 94-151.
23. J. SHI and R. SHIVAJI, 'Global bifurcation for concave semipositon problems', Advances in evolution equations: Proceedings in honor of J. A. Goldstein's 60th birthday (ed. G. R. Goldstein, R. Nagel and S. Romanelli, Marcel Dekker, Inc., New York/Basel, 2003) 385-398.
24. G. SWEERS, 'On the maximum of solutions for a semilinear elliptic problem', Proc. Roy. Soc. Edinburgh Sect. A 108 (1988) 357-370.