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Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains
1. | Dipartimento di Matematica, Università degli Studi di Bari "Aldo Moro", Via E. Orabona 4, 70125 Bari, Italy, Italy |
References:
[1] |
A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in cri\-ti\-cal point theory and applications,, J. Funct. Anal., 14 (1973), 349.
|
[2] |
A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications,, Trans. Amer. Math. Soc., 267 (1981), 1.
|
[3] |
A. Bahri and P.L. Lions, Morse index of some mini-max critical points,, Comm. Pure Appl. Math., 41 (1988), 1027.
|
[4] |
H. Berestycki and P.L. Lions, Nonlinear scalar field equations, I and II,, Arch. Rat. Mech. Anal., 82 (1983), 313.
|
[5] |
F.A. Berezin and M.A. Shubin, The Schr\"odinger equation,, Mathematics and its Applications (Soviet Series) 66, (1991).
|
[6] |
P. Bolle, On the Bolza Problem,, J. Differential Equations, 152 (1999), 274.
|
[7] |
P. Bolle, N. Ghoussoub and H. Tehrani, The multiplicity of solutions in non-homogeneous boundary value problems,, Manuscripta Math., 101 (2000), 325.
|
[8] |
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations,, Springer, (2011).
|
[9] |
A.M. Candela, G. Palmieri and A. Salvatore, Radial solutions of semilinear elliptic equations with broken symmetry,, Topol. Methods Nonlinear Anal., 27 (2006), 117.
|
[10] |
A.M. Candela and A. Salvatore, Multiplicity results of an elliptic equation with non-homogeneous boundary conditions,, Topol. Methods Nonlinear Anal., 11 (1998), 1.
|
[11] |
A.M. Candela, A. Salvatore and M. Squassina, Semilinear elliptic systems with lack of symmetry,, Dynam. Contin. Discrete Impuls. Systems Ser. A, 10 (2003), 181.
|
[12] |
M. Clapp, Y. Ding and S. Hern\`andez-Linares, Strongly indefinite functionals with perturbed symmetries and multiple solutions of non symmetric elliptic systems,, Electron. J. Differential Equations, 100 (2004), 1.
|
[13] |
S.I. Pohozaev, On the global fibering method in nonlinear variational problems,, Proc. Steklov Inst. Math., 219 (1997), 281.
|
[14] |
P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations,, CBMS Regional Conference Series in Mathematics, 65 (1986).
|
[15] |
P.H. Rabinowitz, Multiple critical points of perturbed symmetric functionals,, Trans. Amer. Math. Soc., 272 (1982), 753.
|
[16] |
A. Salvatore, Multiple radial solutions for a superlinear elliptic problem in $\mathbb R^N$,, Dynam. Systems and Applications, 4 (2004), 472.
|
[17] |
W.A. Strauss, Existence of solitary waves in higher dimensions,, Commun. Math. Phys., 55 (1977), 149.
|
[18] |
M. Struwe, Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems,, Manuscripta Math., 32 (1980), 335.
|
[19] |
K. Tanaka, Morse indices at critical points related to the Symmetric Mountain Pass Theorem and applications,, Comm. Partial Differential Equations, 14 (1989), 99.
|
show all references
References:
[1] |
A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in cri\-ti\-cal point theory and applications,, J. Funct. Anal., 14 (1973), 349.
|
[2] |
A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications,, Trans. Amer. Math. Soc., 267 (1981), 1.
|
[3] |
A. Bahri and P.L. Lions, Morse index of some mini-max critical points,, Comm. Pure Appl. Math., 41 (1988), 1027.
|
[4] |
H. Berestycki and P.L. Lions, Nonlinear scalar field equations, I and II,, Arch. Rat. Mech. Anal., 82 (1983), 313.
|
[5] |
F.A. Berezin and M.A. Shubin, The Schr\"odinger equation,, Mathematics and its Applications (Soviet Series) 66, (1991).
|
[6] |
P. Bolle, On the Bolza Problem,, J. Differential Equations, 152 (1999), 274.
|
[7] |
P. Bolle, N. Ghoussoub and H. Tehrani, The multiplicity of solutions in non-homogeneous boundary value problems,, Manuscripta Math., 101 (2000), 325.
|
[8] |
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations,, Springer, (2011).
|
[9] |
A.M. Candela, G. Palmieri and A. Salvatore, Radial solutions of semilinear elliptic equations with broken symmetry,, Topol. Methods Nonlinear Anal., 27 (2006), 117.
|
[10] |
A.M. Candela and A. Salvatore, Multiplicity results of an elliptic equation with non-homogeneous boundary conditions,, Topol. Methods Nonlinear Anal., 11 (1998), 1.
|
[11] |
A.M. Candela, A. Salvatore and M. Squassina, Semilinear elliptic systems with lack of symmetry,, Dynam. Contin. Discrete Impuls. Systems Ser. A, 10 (2003), 181.
|
[12] |
M. Clapp, Y. Ding and S. Hern\`andez-Linares, Strongly indefinite functionals with perturbed symmetries and multiple solutions of non symmetric elliptic systems,, Electron. J. Differential Equations, 100 (2004), 1.
|
[13] |
S.I. Pohozaev, On the global fibering method in nonlinear variational problems,, Proc. Steklov Inst. Math., 219 (1997), 281.
|
[14] |
P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations,, CBMS Regional Conference Series in Mathematics, 65 (1986).
|
[15] |
P.H. Rabinowitz, Multiple critical points of perturbed symmetric functionals,, Trans. Amer. Math. Soc., 272 (1982), 753.
|
[16] |
A. Salvatore, Multiple radial solutions for a superlinear elliptic problem in $\mathbb R^N$,, Dynam. Systems and Applications, 4 (2004), 472.
|
[17] |
W.A. Strauss, Existence of solitary waves in higher dimensions,, Commun. Math. Phys., 55 (1977), 149.
|
[18] |
M. Struwe, Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems,, Manuscripta Math., 32 (1980), 335.
|
[19] |
K. Tanaka, Morse indices at critical points related to the Symmetric Mountain Pass Theorem and applications,, Comm. Partial Differential Equations, 14 (1989), 99.
|
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