Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in ${ℝ}^N$

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1. [1] S. Alama - Y.Y. Li, Existence of solutions for semilinear elliptic equations with indefinite linear part, J. Differential Equations96 (1992), 88-115. Zbl0766.35009MR1153310
2. [2] F. Alessio - P. Montecchiari, Multibump solutions for a class of Lagrangian systems slowly oscillating at infinity, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0919.34044MR1668564
3. [3] F. Alessio - P. Caldiroli - P. Montecchiari, Genericity of the multibump dynamics for almost periodic Duffing-like systems, Proc. Roy. Soc. Edinburgh Sect. A, to appear. Zbl0941.34032MR1719214
4. [4] A. Ambrosetti - M. Badiale, Homoclinics: Poincarè-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998), 232-252. Zbl1004.37043MR1614571
5. [5] A. Ambrosetti - M. Badiale - S. Cingolani, Semiclassical states of nonlinear Schrodinger equation, Arch. Rational Mech. Anal.140 (1997), 285-300. Zbl0896.35042MR1486895
6. [6] S. Angenent, The Shadowing Lemma for Elliptic PDE, Dynamics of Infinite Dimensional Systems (S.N. Chow and J.K. Hale eds.) F37 (1987), 6-22. Zbl0653.35030MR921893
7. [7] A. Bahri - Y.Y. Li, On a AIin-Max Procedure for the Existence of a Positive Solution for Certain Scalar Field Equation in Rn, Rev. Mat. Iberoamericana6 (1990), 1-15. Zbl0731.35036MR1086148
8. [8] A. Bahri - P.L. Lions, On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire14 (1997), 365-413. Zbl0883.35045MR1450954
9. [9] H. Berestycki - P.L. Lions, Nonlinear scalar field equations, Arch. Rational Mech. Anal.82 (1983), 313-345. Zbl0556.35046MR695535
10. [10] A.S. Besicovitch, "Almost Periodic Functions", Dover Pubblications Inc. (1954). Zbl0065.07102MR68029
11. [11] D.M. Cao, Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equation in Rn, Nonlinear Anal. 15 (1990), 1045-1052. Zbl0729.35049MR1082280
12. [12] D.M. Cao, Multiple solutions of a semilinear elliptic equation in Rn, Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993), 593-604. Zbl0797.35039MR1253603
13. [13] D.M. Cao - E.S. Noussair, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in Rn, Ann. Inst. H. Poincaré Anal. Non Linéaire13 (1996), 567-588. Zbl0859.35032MR1409663
14. [14] V. Coti Zelati - I. Ekeland - E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann.288 (1990), 133-160. Zbl0731.34050MR1070929
15. [15] V. Coti Zelati - P.H. Rabinowitz, Homoclinic type solutions for a semilinear elliptic PDE on Rn, Comm. Pure Appl. Math.45 (1992), 1217-1269. Zbl0785.35029MR1181725
16. [16] M. Del Pino - P.L. Felmer, Multi-peak bound states for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998), 127-149. Zbl0901.35023MR1614646
17. [17] W.Y. Ding - W.M. Ni, On the existence of a positive entire solution of a semilinear elliptic equation, Arch. Rational Mech. Anal.91 (1986), 283-308. Zbl0616.35029MR807816
18. [18] M.J. Esteban - P.L. Lions, Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect.A93 (1982), 1-14. Zbl0506.35035MR688279
19. [19] C. Gui, Existence of multi-bump solutions for nonlinear Schrödinger equations via variational methods, Comm. Partial Differential Equations21 (1996), 787-820. Zbl0857.35116MR1391524
20. [20] Y. Li, Remarks on a semilinear elliptic equation on RN, J. Differential Equations74 (1988), 34-39. Zbl0662.35038MR949624
21. [21] Y.Y. Li, Prescribing scalar curvature on S3,S4 and related problems, J. Funct. Anal.118 (1993),43-118. Zbl0790.53040MR1245597
22. [22] Y.Y. Li, On a singularly perturbed elliptic equation, Adv. Differential Equations2 (1997), 955-980. Zbl1023.35500MR1606351
23. [23] P.L. Lions, The concentration-compactness principle in the calculus of variations: the locally compact case, Part I and II, Ann. Inst. H. Poincaré Anal. Non Linéaire1 (1984), 109-145 and 223-283. Zbl0704.49004
24. [24] P. Montecchiari, Multiplicity results for a class of Semilinear Elliptic Equations on Rm, Rend. Sem. Mat. Univ. Padova95 (1996), 1-36. Zbl0866.35043MR1405365
25. [25] R. Musina, Multiple positive solutions of a scalar field equation in Rn, Topol. Methods Nonlinear Anal.7 (1996), 171-185. Zbl0909.35042MR1422010
26. [26] W.M. Ni, Some aspects of semilinear elliptic equations, Nonlinear diffusion equations and their equilibrium states (W.M. Ni, L.A. Peletier and J. Serrin, eds.) Springer Verlag, Berlin (1988), 171-215. Zbl0676.35026MR956087
27. [27] P.H. Rabinowitz, A note on a semilinear elliptic equation on Rn, Nonlinear Analysis, a tribute in honour of Giovanni Prodi (A. Ambrosetti and A. Marino, eds., Quademi della Scuola Normale Superiore, Pisa) (1991), 307-317. Zbl0836.35045MR1205391
28. [28] P.H. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys.43 (1992), 270-291. Zbl0763.35087MR1162728
29. [29] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993), 561-590. Zbl0803.58013MR1249107
30. [30] W.A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1979), 149-162. Zbl0356.35028MR454365
31. [31] C.A. Stuart, Bifurcation in LP(Rn) for a semilinear elliptic equation, Proc. London Math. Soc. (3) 57 (1988), 511-541. Zbl0673.35005MR960098

1. Francesca Alessio, Paolo Caldiroli, Piero Montecchiari, On the existence of infinitely many solutions for a class of semilinear elliptic equations in ${\mathbb{R}}^N$
2. Francesca Alessio, Paolo Caldiroli, Piero Montecchiari, Infinitely many solutions for a class of semilinear elliptic equations in ${\mathbb{R}}^N$