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Infinitely many solutions for an elliptic problem with double critical Hardy-Sobolev-Maz'ya terms
On the shape Conley index theory of semiflows on complete metric spaces
1. | Department of Math., School of Science, Tianjin University, Tianjin 300072, China |
2. | Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072 |
3. | Department of Applied Math., Illinois Institute of Technology, Chicago IL 60616, United States |
References:
[1] |
K. Borsuk, Theory of Shape, Monografie Matematyczne, Tom 59 [Mathematical Monographs, Vol. 59], PWN-Polish Scientific Publishers, Warsaw, 1975. |
[2] |
C. Conley, Isolated Invariant Sets and the Morse Index, Regional Conference Series in Mathematics, 38, American Mathematical Society, Providence, RI, 1978. |
[3] |
J. Dydak and J. Segal, Shape Theory: An Introduction, Lecture Notes in Math., 688, Springer-Verlag, Berlin, 1978. |
[4] |
A. Giraldo, M. A. Morón, F. R. Ruiz del Portal and J. M. R. Sanjurjo, Shape of global attractors in topological spaces, Nonlinear Anal., 60 (2005), 837-847.
doi: 10.1016/j.na.2004.03.036. |
[5] |
A. Giraldo, R. Jiménez, M. A. Morón, F. R. Ruiz del Portal and J. M. R. Sanjurjo, Pointed shape and global attractors for metrizable spaces, Topology Appl., 158 (2011), 167-176.
doi: 10.1016/j.topol.2010.08.015. |
[6] |
A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. |
[7] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[8] |
L. Kapitanski and I. Rodnianski, Shape and Morse theory of attractors, Comm. Pure Appl. Math., 53 (2000), 218-242.
doi: 10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W. |
[9] |
D. Li, Morse theory of attractors via Lyapunov functions, preprint,, , ().
|
[10] |
D. Li, G. Shi and X. Song, A linking theory for dynamical systems with applications to PDEs,, , ().
|
[11] |
S. Mardešić and J. Segal, Shape Theory - The Inverse System Approach, North-Holland Mathematical Library, 26, North-Holland, Amsterdam-New York, 1982. |
[12] |
M. Mrozek, Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces, Fund. Math., 145 (1994), 15-37. |
[13] |
J. W. Robbin and D. Salamon, Dynamical systems, shape theory and the Conley index, Ergodic Theory Dynam. Systems, 8 (1988), 375-393.
doi: 10.1017/S0143385700009494. |
[14] |
K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer-Verlag, Berlin, 1987.
doi: 10.1007/978-3-642-72833-4. |
[15] |
J. J. Sánchez-Gabites, An approach to the Conley shape index without index pairs, Rev. Mat. Complut., 24 (2011), 95-114.
doi: 10.1007/s13163-010-0031-x. |
[16] |
J. M. R. Sanjurjo, Morse equation and unstable manifolds of isolated invariant set, Nonlinearity, 16 (2003), 1435-1448.
doi: 10.1088/0951-7715/16/4/314. |
[17] |
J. M. R. Sanjurjo, Shape and Conley index of attractors and isolated invariant sets, Progress Nonlinear Diff. Eqns., 75 (2008), 393-406.
doi: 10.1007/978-3-7643-8482-1_29. |
[18] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, $2^{nd}$ edition, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
show all references
References:
[1] |
K. Borsuk, Theory of Shape, Monografie Matematyczne, Tom 59 [Mathematical Monographs, Vol. 59], PWN-Polish Scientific Publishers, Warsaw, 1975. |
[2] |
C. Conley, Isolated Invariant Sets and the Morse Index, Regional Conference Series in Mathematics, 38, American Mathematical Society, Providence, RI, 1978. |
[3] |
J. Dydak and J. Segal, Shape Theory: An Introduction, Lecture Notes in Math., 688, Springer-Verlag, Berlin, 1978. |
[4] |
A. Giraldo, M. A. Morón, F. R. Ruiz del Portal and J. M. R. Sanjurjo, Shape of global attractors in topological spaces, Nonlinear Anal., 60 (2005), 837-847.
doi: 10.1016/j.na.2004.03.036. |
[5] |
A. Giraldo, R. Jiménez, M. A. Morón, F. R. Ruiz del Portal and J. M. R. Sanjurjo, Pointed shape and global attractors for metrizable spaces, Topology Appl., 158 (2011), 167-176.
doi: 10.1016/j.topol.2010.08.015. |
[6] |
A. Hatcher, Algebraic Topology, Cambridge University Press, 2002. |
[7] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[8] |
L. Kapitanski and I. Rodnianski, Shape and Morse theory of attractors, Comm. Pure Appl. Math., 53 (2000), 218-242.
doi: 10.1002/(SICI)1097-0312(200002)53:2<218::AID-CPA2>3.0.CO;2-W. |
[9] |
D. Li, Morse theory of attractors via Lyapunov functions, preprint,, , ().
|
[10] |
D. Li, G. Shi and X. Song, A linking theory for dynamical systems with applications to PDEs,, , ().
|
[11] |
S. Mardešić and J. Segal, Shape Theory - The Inverse System Approach, North-Holland Mathematical Library, 26, North-Holland, Amsterdam-New York, 1982. |
[12] |
M. Mrozek, Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces, Fund. Math., 145 (1994), 15-37. |
[13] |
J. W. Robbin and D. Salamon, Dynamical systems, shape theory and the Conley index, Ergodic Theory Dynam. Systems, 8 (1988), 375-393.
doi: 10.1017/S0143385700009494. |
[14] |
K. P. Rybakowski, The Homotopy Index and Partial Differential Equations, Springer-Verlag, Berlin, 1987.
doi: 10.1007/978-3-642-72833-4. |
[15] |
J. J. Sánchez-Gabites, An approach to the Conley shape index without index pairs, Rev. Mat. Complut., 24 (2011), 95-114.
doi: 10.1007/s13163-010-0031-x. |
[16] |
J. M. R. Sanjurjo, Morse equation and unstable manifolds of isolated invariant set, Nonlinearity, 16 (2003), 1435-1448.
doi: 10.1088/0951-7715/16/4/314. |
[17] |
J. M. R. Sanjurjo, Shape and Conley index of attractors and isolated invariant sets, Progress Nonlinear Diff. Eqns., 75 (2008), 393-406.
doi: 10.1007/978-3-7643-8482-1_29. |
[18] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, $2^{nd}$ edition, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
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