Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in N
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, p. 47-68
@article{ASNSP_1998_4_27_1_47_0,
     author = {Alessio, Francesca and Caldiroli, Paolo and Montecchiari, Piero},
     title = {Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in $\mathbb {R}^N$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 27},
     number = {1},
     year = {1998},
     pages = {47-68},
     zbl = {0931.35047},
     mrnumber = {1658893},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_27_1_47_0}
}
Alessio, Francesca; Caldiroli, Paolo; Montecchiari, Piero. Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in $\mathbb {R}^N$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, pp. 47-68. http://www.numdam.org/item/ASNSP_1998_4_27_1_47_0/

[1] S. Alama - Y.Y. Li, Existence of solutions for semilinear elliptic equations with indefinite linear part, J. Differential Equations 96 (1992), 88-115. | MR 1153310 | Zbl 0766.35009

[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. | Numdam | MR 1668564 | Zbl 0919.34044

[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. | MR 1719214 | Zbl 0941.34032

[4] A. Ambrosetti - M. Badiale, Homoclinics: Poincarè-Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 232-252. | Numdam | MR 1614571 | Zbl 1004.37043

[5] A. Ambrosetti - M. Badiale - S. Cingolani, Semiclassical states of nonlinear Schrodinger equation, Arch. Rational Mech. Anal. 140 (1997), 285-300. | MR 1486895 | Zbl 0896.35042

[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. | MR 921893 | Zbl 0653.35030

[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. Iberoamericana 6 (1990), 1-15. | MR 1086148 | Zbl 0731.35036

[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 Linéaire 14 (1997), 365-413. | Numdam | MR 1450954 | Zbl 0883.35045

[9] H. Berestycki - P.L. Lions, Nonlinear scalar field equations, Arch. Rational Mech. Anal. 82 (1983), 313-345. | MR 695535 | Zbl 0533.35029 | Zbl 0556.35046

[10] A.S. Besicovitch, "Almost Periodic Functions", Dover Pubblications Inc. (1954). | MR 68029 | Zbl 0065.07102

[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. | MR 1082280 | Zbl 0729.35049

[12] D.M. Cao, Multiple solutions of a semilinear elliptic equation in Rn, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 593-604. | Numdam | MR 1253603 | Zbl 0797.35039

[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 Linéaire 13 (1996), 567-588. | Numdam | MR 1409663 | Zbl 0859.35032

[14] V. Coti Zelati - I. Ekeland - E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 288 (1990), 133-160. | MR 1070929 | Zbl 0731.34050

[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. | MR 1181725 | Zbl 0785.35029

[16] M. Del Pino - P.L. Felmer, Multi-peak bound states for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998), 127-149. | Numdam | MR 1614646 | Zbl 0901.35023

[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. | MR 807816 | Zbl 0616.35029

[18] M.J. Esteban - P.L. Lions, Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 1-14. | MR 688279 | Zbl 0506.35035

[19] C. Gui, Existence of multi-bump solutions for nonlinear Schrödinger equations via variational methods, Comm. Partial Differential Equations 21 (1996), 787-820. | MR 1391524 | Zbl 0857.35116

[20] Y. Li, Remarks on a semilinear elliptic equation on RN, J. Differential Equations 74 (1988), 34-39. | MR 949624 | Zbl 0662.35038

[21] Y.Y. Li, Prescribing scalar curvature on S3,S4 and related problems, J. Funct. Anal. 118 (1993),43-118. | MR 1245597 | Zbl 0790.53040

[22] Y.Y. Li, On a singularly perturbed elliptic equation, Adv. Differential Equations 2 (1997), 955-980. | MR 1606351 | Zbl 1023.35500

[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 Linéaire 1 (1984), 109-145 and 223-283. | Numdam | Zbl 0704.49004

[24] P. Montecchiari, Multiplicity results for a class of Semilinear Elliptic Equations on Rm, Rend. Sem. Mat. Univ. Padova 95 (1996), 1-36. | Numdam | MR 1405365 | Zbl 0866.35043

[25] R. Musina, Multiple positive solutions of a scalar field equation in Rn, Topol. Methods Nonlinear Anal. 7 (1996), 171-185. | MR 1422010 | Zbl 0909.35042

[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. | MR 956087 | Zbl 0676.35026

[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. | MR 1205391 | Zbl 0836.35045

[28] P.H. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992), 270-291. | MR 1162728 | Zbl 0763.35087

[29] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 561-590. | Numdam | MR 1249107 | Zbl 0803.58013

[30] W.A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1979), 149-162. | MR 454365 | Zbl 0356.35028

[31] C.A. Stuart, Bifurcation in LP(Rn) for a semilinear elliptic equation, Proc. London Math. Soc. (3) 57 (1988), 511-541. | MR 960098 | Zbl 0673.35005