Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth

Discrete and Continuous Dynamical Systems

Volumn 7, Issue 4, 2001, Pages 703-718

  Grossi, M ^a   Magrone, P ^b   Matzeu, M ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Critical exponent; Linking type critical points; Potential changing sign

Indexed keywords

EID: 0035610445     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2001.7.703     Document Type: Article

References (22)

1. S. Alama and M. del Pino, Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking, Ann. I.H.P. Analyse non lineaire 13 (1996), 95-115.
2. S. Alama and G. Tarantello, On semilinear elliptic equations with indefinite nonlinearities, Calc. Var. 1 (1993), 439-475.
3. S. Alama and G. Tarantello, Elliptic problems with nonlinearities indefinite in sign, J. Funct. An. 141 (1996), 159-215.
4. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. An. 14 (1973), 349-381.
5. M. Badiale, Infinitely many solutions for some indefinite nonlinear elliptic problems, Comm. on Appl. Non. Anal. 3 (1996), 61-76.
6. M. Badiale and E. Nabana, A remark on multiplicity solutions for semilinear elliptic problems with indefinite nonlinearities, C.R. Acad. Sc. Paris 323 serie 1 (1996), 151-156.
7. H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg, Variational methods for indefinite superlinear homogeneous elliptic systems, NoDEA 2 (1995), 533-572.
8. H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topological Methods in Nonlinear Analysis 4 (1994), 59-78.
9. H. Brexis and J.M. Coron, Convergence of Solutions of H-Systems or How to Blow Bubbles, Arch. Rational Mech. Anal. 89 (1985), 21-56..
10. H. Brezis and T. Kato, Remarks on the Schrödinger operator with singular complex potential, J. math. Pures Appl. 58 (1979), 137-151.
11. H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. AMS 88 (1983), 486-490.
12. H. Brezis and L. Nirenberg, Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents, Comm. Pure Appl. Math. XXXVI (1983), 437-477.
13. A. Capozzi, D. Fortunato and G. Palmieri, An existence result for nonlinear elliptic problems involving critical sobolev exponent, Ann. I.H.P., Analyse non linaire 2 (1985), 463-470.
14. G. Cerami, D. Fortunato and M. Struwe, Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents, Ann. I.H.P. Analyse non lineaire 1 (1984), 341-350.
15. M. Girardi, M. Matzeu, Existence and multiplicity results for periodic solutions of superquadratic Hamiltonian Systems where the potential changes sign, NoDEA 2 (1995), 35-61.
16. P.L. Lions, The concentration compactness principle in the calculus of variation: the limit case. Rev. Math. Iberoamericana 1 (1985), n. 1, 145-201.
17. P.L. Lions, The concentration compactness principle in the calculus of variation: the limit case, Rev. Math. Iberoamericana 1 (1985), n. 2, 45-121.
18. P. Magrone, On a class on semilinear elliptic equations with potential changing sign, Dynamical Systems and Appl. 9 (2000), 459-168.
19. P.H. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partial differential equations, Ann.Sc.Norm.Sup. Pisa cl.Sci. 4 (1978).
20. M. Ramos, S. Terracini and C. Troestler, Superlinear indefinite elliptic problems and Pohozaev type identities, J. Funct. Anal. 159 (1998), 596-628.
21. M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 (1984), 511-517.
22. H.T. Tehrani, Infinitely many solutions for indefinite semilinear elliptic equations without symmetries, Comm. in PDE 21 (1996), 541-557.