Compact invariant sets for some quasilinear nonlocal Kirchhoff strings on ℝ^N

References

• Kirchhoff , G . 1883 . Vorlesungen Über Mechanik , Leipzig : Teubner .
   Google Scholar
• Ghidaglia , JM and Temam , R . 1987 . Attractors for damped nonlinear wave equations . Journal de Mathématiques Pures et Appliquées , 66 : 273 – 319 .
   Web of Science ®Google Scholar
• Ladyzenskaja , OA . 1987 . On the determination of minimal global attractors for the Navier-Stokes equations and other partial differential equations . Uspekhi Matematicheskikh Nauk , 42 : 25 – 60 . [English Translation: Russian Mathematical Surveys, 42, 27–73.]
   Google Scholar
• Babin , AV and Vishik , MI . 1990 . Attractors for partial differential evolution eguations in an unbounded domain . Proceedings of the Royal Society of Edinburgh , 116A : 221 – 243 .
   Google Scholar
• Hale , JK . 1988 . “ Asymptotic behaviour of dissipative systems ” . In Mathematical Surveys and Monographs 25 , AMS : Providence, RI .
   Google Scholar
• Haraux , A . 1991 . “ Systemes dynamiques dissipatifs et applications ” . In RMA 17 , Paris : Masson .
   Google Scholar
• Temam , R . 1997 . “ Infinite-dimensional dynamical systems in mechanics and physics ” . In Applications in Mathematical Science , 2nd , Vol. 68 , New York : Springer-Verlag .
   Google Scholar
• Ono , K . 1997 . On global existence, asymptotic stability and blowing–up of solutions for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation . Mathematical Methods in Applied Science , 20 : 151 – 177 .
   Web of Science ®Google Scholar
• Ono , K . 1997 . Global existence and decay properties of solutions for some mildly degenerate nonlinear dissipative Kirchhoff strings . Funkcialaj Ekvacioj , 40 : 255 – 270 .
   Google Scholar
• Ono , K . 1997 . Global existence, decay, and blow-up of solutions for some mildly degenerate nonlinear Kirchhoff strings . Journal of Differential Equations , 137 : 273 – 301 .
   Web of Science ®Google Scholar
• Babin , AV and Vishik , MI . 1992 . Attractors for evolution equations , Amsterdam : North-Holland .
   Google Scholar
• Brenner , P . 1989 . On space-time means and strong global solutions on nonlinear hyperbolic equations . Mathematische Zeitschrift , 201 : 45 – 55 .
   Web of Science ®Google Scholar
• Feiresl , E . 1994 . Attractors for semilinear damped wave equations on R 3 . Nonlinear Analysis TMA , 23 ( 2 ) : 187 – 195 .
   Google Scholar
• Feiresl , E . 1995 . Asymptotic behaviour and attractors for a semilinear damped wave equations with supercritical exponent . Proceedings of the Royal Society Edinburgh , 125A : 1051 – 1062 .
   Google Scholar
• Karachalios , NI and Stavrakakis , NM . 1999 . Existence of global attractors for semilinear dissipative wave equations on ℝ N . Journal of Differential Equations , 157 : 183 – 205 .
   Google Scholar
• Karachalios , NI and Stavrakakis , NM . 2001 . Global existence and blow-up results for some nonlinear wave equations on ℝ N . Advances in Differential Equations , 6 : 155 – 174 .
   Google Scholar
• Karachalios , NI . 2002 . Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on ℝ N . Discrete and Continuous Dynamical Systems , 8 : 939 – 951 .
   Google Scholar
• Papadopoulos , PG and Stavrakakis , NM . 2001 . Global existence and blow-up results for an equation of Kirchhoff type on ℝ N . Topological Methods in Nonlinear Analysis , 17 : 91 – 109 .
   Google Scholar
• Brown , KJ and Stavrakakis , NM . 1996 . Global bifurcation results for a semilinear elliptic equation on all of ℝ N . Duke Mathematical Journal , 85 : 77 – 94 .
   Web of Science ®Google Scholar
• Zeidler , E . 1990 . “ Nonlinear Functional Analysis and its Applications ” . In Monotone Operators , Vol. II , New York : Springer-Verlag .
   Google Scholar
• Henry , D . 1981 . “ Geometric Theory of Semilinear Parabolic Equations ” . In Lecture Notes in Mathematics , Berlin : Springer-Verlag .
   Google Scholar