On a nonlinear elliptic system: resonance and bifurcation cases

 Access to full text

 Full (PDF)

 Access to full text

1. Ahmad S., Lazer A., Paul J., Elementary critical point theory and perturbation of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933-944. (1976) MR0427825
2. Ambrosetti A., Mancini G., Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue, J. Diff. Equations 28 (1978), 220-245. (1978) Zbl0393.35032MR0492839
3. Anane A., Etude des valeurs propers et la resonance pour le operateur P-Laplacian, Ph.D. Thesis, Univ. Bruxelles, 1988. 
4. Bartolo P., Benci V., Fortunato D., Abstract critical point Theorems and applications to some nonlinear problems with strong resonance, Nonlinear Analysis T.M.A. 7 9 (1983), 981-1012. (1983) Zbl0522.58012MR0713209
5. Berestycki H., Defigueiredo D., Double resonance in semilinear elliptic problems, Comm. Partial Diff. Equations 6 91-120 (1981). (1981) MR0597753
6. Brown K.J., Spatially inhomogeneous steady-state solutions for systems of equations describing interacting populations, J. Math. Anal. Appl. 95 (1983), 251-264. (1983) Zbl0518.92017MR0710432
7. Capozzi A., Lupo D., Solimini S., On the existence of a nontrivial solution to nonlinear problem at resonance, Nonlinear Analysis T.M.A. 13 2 151-163 (1989). (1989) MR0979038
8. Cesari L., Kannan R., Qualitative study of a class of nonlinear boundary value problems at resonance, J. Diff. Equations 56 63-81 (1985). (1985) Zbl0554.34009MR0772121
9. Chiappinelli R., Mawhin J., Nugari R., Bifurcation from infinity and multiple solutions for some Dirichlet problems with unbounded nonlinearities, Nonlinear Analysis T.M.A, in press. Zbl0780.35038
10. Chow S., Hale J., Methods of Bifurcation Theory, Springer Verlag (1982). (1982) Zbl0487.47039MR0660633
11. Costa D., Magalh aes, A variational approach to subquadratic perturbations of elliptic systems, J. Diff. Equations 111 1 103-122 (1994). (1994) MR1280617
12. De Figueiredo D., Chiappinelli R., Bifurcation from infinity and multiple solutions for an elliptic system, Differential and Integral Equations 6 4 (1993), 757-771. (1993) Zbl0784.35008MR1222299
13. De Figueiredo D., Gossez J., Resonance below the first eigenvalue for a semilinear elliptic problem, Math. Ann. 281 589-610 (1988). (1988) MR0958261
14. De Figueiredo D., Mitidieri E., A maximum principle for an elliptic system and applications to semilinear problems, Siam. J. Math. Anal. 17 (1986), 836-849. (1986) Zbl0608.35022MR0846392
15. Gossez J., Some nonlinear differential equations at resonance at first eigenvalue, Conf. Sem. Mat. Univ Bari 167 355-389 (1979). (1979) 
16. Hernández J., Maximum Principles and Decoupling for Positive Solutions of Reaction-Diffusion Systems, Oxford University Press, K.J. Brown and A. Lacey eds, 1990, pp.199-224. MR1086647
17. Iannacci R., Nkashama M., Nonlinear boundary value problems at resonance, Nonlinear Analysis T.M.A. 11 455-473 (1987). (1987) Zbl0676.35023MR0887655
18. Iannacci R., Nkashama M., Nonlinear second order elliptic partial differential equations at resonance, Report 87-12, Memphis State University, 1987. Zbl0686.35045
19. Krasnosels'kii M., Zabreico F., Geometrical Methods of Nonlinear Analysis, Springer Verlag (1984). (1984) MR0736839
20. Landesman E., Lazer A., Nonlinear perturbation of elliptic boundary value problems at resonance, J. Math. Mech. 19 609-623 (1970). (1970) MR0267269
21. Lazer A., McKenna P.J., On steady-state solutions of a system of reaction-diffusion equations from biology, Nonlinear Analysis T.M.A. 6 (1982), 523-530. (1982) Zbl0488.35039MR0664014
22. Lupo D., Solimini S., A note on a resonance problem, Proc. Royal Soc. Edinburgh 102 A 1-7 (1986). (1986) Zbl0593.35036MR0837156
23. Mawhin J., Bifurcation from infinity and nonlinear boundary value problems, in ordinary and partial differential equations, vol. II, Sleeman and Jarvis eds, Longman, Ifarlow, 1989, pp.119-129. MR1031727
24. Mawhin J., Schmitt K., Landesman-Lazer type problems at an eigenvalue of odd multiplicity, Results in Math. 14 (1988), 138-146. (1988) Zbl0780.35043MR0956010
25. Mawhin J., Schmitt K., Nonlinear eigenvalue problems with the parameter near resonance, Ann. Polon. Math. 51 (1990), 241-248. (1990) Zbl0724.34025MR1093994
26. Omari P., Zanolin F., A note on nonlinear oscillations at resonance, Acta Math. Sinica 3 351-361 (1987). (1987) Zbl0648.34040MR0930765
27. Rabinowitz P., Minimax methods in critical point theory with applications to differential equations, CBMS 65 Regional Conference Series in Math, A.M.S., 1986. Zbl0609.58002MR0845785
28. Rothe F., Global existence of branches of stationary solutions for a system of reaction-diffusion equations from biology, Nonlinear Analysis T.M.A. 5 (1981), 487-498. (1981) Zbl0471.35031MR0613057
29. Schechter M., Nonlinear elliptic boundary value problems at resonance, Nonlinear Analysis T.M.A. 14 10 889-903 (1990). (1990) Zbl0708.35033MR1055536
30. Smoller J., Shock Waves and Reaction-Diffusion Equations, Springer-Verlag (1983). (1983) Zbl0508.35002MR0688146
31. Solimini S., On the solvability of some elliptic partial differential equations with the linear part at resonance, J. Math. Anal. Appl. 117 138-152 (1986). (1986) Zbl0634.35030MR0843010
32. Vargas C., Zuluaga M., On a nonlinear Dirichlet problem type at resonance and bifurcation, Partial Differential Equations Pitmann Research Notes in Math. Series 273, pp.248-252 (1992). (1992) Zbl0795.35035
33. Vargas C., Zuluaga M., A nonlinear elliptic problem at resonance with a nonsimple eigenvalue, Nonlinear Analysis T.M.A. (1996), 711-721. (1996) Zbl0861.35030MR1399070
34. Zuluaga M., A nonlinear elliptic system at resonance, Dynamic Systems and Applications 3 4 501-510 (1994). (1994) Zbl0811.35037MR1304129
35. Zuluaga M., Nonzero solutions of a nonlinear elliptic system at resonance, Nonlinear Analysis T.M.A 31 3/4 445-454 (1996). (1996) MR1487555

1. Mario Zuluaga Uribe, Nonzero and positive solutions of a superlinear elliptic system