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On a functional satisfying a weak Palais-Smale condition
| 1. | Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, I-85100 Potenza |
References:
| [1] |
R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, Vol. 65. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
| [2] |
A. Azzollini, P. d'Avenia and A. Pomponio, Quasilinear elliptic equations in $\mathbbR^N$ via variational methods and Orlicz-Sobolev embeddings,, Calc. Var. (to appear)., ().
doi: 10.1007/s00526-012-0578-0. |
| [3] |
A. Azzollini and A. Pomponio, On the Schrödinger equation in $\mathbbR^N$ under the effect of a general nonlinear term, Indiana Univ. Math. Journal, 58 (2009), 1361-1378.
doi: 10.1512/iumj.2009.58.3576. |
| [4] |
M. Badiale, L. Pisani and S. Rolando, Sum of weighted Lebesgue spaces and nonlinear elliptic equations, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 369-405.
doi: 10.1007/s00030-011-0100-y. |
| [5] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorem and applications to some nonlinear problems with "strong'' resonance at infinity, Nonlin. Anal. TMA, 7 (1983), 981-1012.
doi: 10.1016/0362-546X(83)90115-3. |
| [6] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.
doi: 10.1007/BF00250555. |
| [7] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., 82 (1983), 347-375.
doi: 10.1007/BF00250556. |
| [8] |
G. Cerami, Un criterio di esistenza per i punti critici su varietà illimitate, Rc. Ist. lomb. Sci. Lett., 112 (1978), 332-336. |
| [9] |
T. D'Aprile and G. Siciliano, Magnetostatic solutions for a semilinear perturbation of the Maxwell equations, Adv. Differential Equations, 16 (2011), 435-466. |
| [10] |
J. Hirata, N. Ikoma and K. Tanaka, Nonlinear scalar field equations in $\mathbbR^N$: Mountain pass and symmetric mountain pass approaches, TMNA, 35 (2010), 253-276. |
| [11] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer-type problem set on $\mathbbR^N$, Proc. R. Soc. Edinb., Sect. A, Math., 129 (1999), 787-809.
doi: 10.1017/S0308210500013147. |
| [12] |
E. H. Lieb and M. Loss, Analysis, Second edition. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI, 2001. |
| [13] |
M. Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv., 60 (1985), 558-581.
doi: 10.1007/BF02567432. |
show all references
References:
| [1] |
R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, Vol. 65. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
| [2] |
A. Azzollini, P. d'Avenia and A. Pomponio, Quasilinear elliptic equations in $\mathbbR^N$ via variational methods and Orlicz-Sobolev embeddings,, Calc. Var. (to appear)., ().
doi: 10.1007/s00526-012-0578-0. |
| [3] |
A. Azzollini and A. Pomponio, On the Schrödinger equation in $\mathbbR^N$ under the effect of a general nonlinear term, Indiana Univ. Math. Journal, 58 (2009), 1361-1378.
doi: 10.1512/iumj.2009.58.3576. |
| [4] |
M. Badiale, L. Pisani and S. Rolando, Sum of weighted Lebesgue spaces and nonlinear elliptic equations, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 369-405.
doi: 10.1007/s00030-011-0100-y. |
| [5] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorem and applications to some nonlinear problems with "strong'' resonance at infinity, Nonlin. Anal. TMA, 7 (1983), 981-1012.
doi: 10.1016/0362-546X(83)90115-3. |
| [6] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.
doi: 10.1007/BF00250555. |
| [7] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., 82 (1983), 347-375.
doi: 10.1007/BF00250556. |
| [8] |
G. Cerami, Un criterio di esistenza per i punti critici su varietà illimitate, Rc. Ist. lomb. Sci. Lett., 112 (1978), 332-336. |
| [9] |
T. D'Aprile and G. Siciliano, Magnetostatic solutions for a semilinear perturbation of the Maxwell equations, Adv. Differential Equations, 16 (2011), 435-466. |
| [10] |
J. Hirata, N. Ikoma and K. Tanaka, Nonlinear scalar field equations in $\mathbbR^N$: Mountain pass and symmetric mountain pass approaches, TMNA, 35 (2010), 253-276. |
| [11] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer-type problem set on $\mathbbR^N$, Proc. R. Soc. Edinb., Sect. A, Math., 129 (1999), 787-809.
doi: 10.1017/S0308210500013147. |
| [12] |
E. H. Lieb and M. Loss, Analysis, Second edition. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI, 2001. |
| [13] |
M. Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv., 60 (1985), 558-581.
doi: 10.1007/BF02567432. |
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