Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
Stanley Alama; Manuel Del Pino
Annales de l'I.H.P. Analyse non linéaire (1996)
- Volume: 13, Issue: 1, page 95-115
- ISSN: 0294-1449
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top- [1] S. Alama and G. Tarantello, On semilinear elliptic equations with indefinite nonlinearities, Calc. of Var. and P. D. E., Vol. 1, 1993, pp. 439-475. Zbl0809.35022MR1383913
- [2] S. Alama and G. Tarantello, On the solvability of a semilinear elliptic equation via an associated eigenvalue problem, to appear inMath. Z. Zbl0853.35039MR1381593
- [3] S. Alama and G. Tarantello, Elliptic problems with nonlinearities indefinite in sign, preprint, 1994. Zbl0860.35032MR1414377
- [4] V. Benci and P. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math., Vol. 52, 1979, pp. 241-273. Zbl0465.49006MR537061
- [5] H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires, C. R. Acad. Sci. Paris, t. 317, Série I, 1993, pp. 945-950. Zbl0820.35056MR1249366
- [6] H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Variational methods for indefinite superlinear homogeneous elliptic problems, preprint, May 1994. MR1356874
- [7] H. Berestycki, I. Capuzzo-Dolcetta and L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, preprint, 1994. Zbl0816.35030MR1321809
- [8] H. Brezis and L. Nirenberg, "H1 versus C1 minimizers", C. R. Acad. Sci. Paris, t. 317, Série I, 1993, pp. 465-572. Zbl0803.35029MR1239032
- [9] K.C. Chang, "Infinite Dimensional Morse Theory and Multiple Solution Problems", Birkhäuser: Boston, 1993. Zbl0779.58005MR1196690
- [10] K.C. Chang, "H1 versus C1 isolated critical points", C. R. Acad. Sci. Paris, t. 319, Série I, 1994, pp. 441-446. Zbl0810.35025MR1296769
- [11] M. Del Pino and P. Felmer, Multiple solutions for a semilinear elliptic equation, preprint, 1992. MR1303117
- [12] J.F. Escobar and R.M. Schoen, Conformal metrics with prescribed scalar curvature, Invent. Math., Vol. 86, 1986, pp. 243-254. Zbl0628.53041MR856845
- [13] H. Hofer, A Note on the Topological Degree at a Critical Point of Mountainpass-type, Proc. Am. Math. Soc., Vol. 90, 1984, pp. 309-315. Zbl0545.58015MR727256
- [14] J. Kazdan and F. Warner, Scalar curvature and the conformal deformation of Riemannian structure, J. Diff. Geom., Vol. 10, 1975, pp. 113-134. Zbl0296.53037MR365409
- [15] J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Springer: New York, 1989. Zbl0676.58017MR982267
- [16] T. Ouyang, On the positive solutions of semilinear elliptic equations Δu + λu + hup = 0 on compact manifolds, Part II, Indiana Univ. Math. J., Vol. 40, 1992, pp. 1083-1140. Zbl0773.35020MR1129343
- [17] P. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations," CBMS-NSF, Vol. 65, American Math. Soc.: Providence, 1986. Zbl0609.58002MR845785
- [18] M. Struwe, "Variational Methods", Springer-Verlag: Berlin, 1990. Zbl0746.49010MR1078018
- [19] H. Tehrani, Ph.D. thesis, New York Univ., 1994.
- [20] Z.Q. Wang, On a superlinear elliptic equation, Ann. Inst. H. Poincaré- Analyse Non lin., Vol. 8, 1991, pp. 43-57. Zbl0733.35043MR1094651