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On the existence and stability of periodic solutions for pendulum-like equations with friction and $\phi$-Laplacian
Some bifurcation results for rapidly growing nonlinearities
| 1. | School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia |
References:
| [1] |
K. C. Chang, "Infinite-dimensional Morse Theory and Multiple Solution Problems," Birkhäuser Boston Inc., Boston, 1993. |
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E. N. Dancer, Global structure of the solutions of non-linear real analytic eigenvalue problems, Proc. London Math. Soc., s3-27 (1973), 747-765.
doi: 10.1112/plms/s3-27.4.747. |
| [3] |
E. N. Dancer, Global solution branches for positive mappings, Arch. Rational Mech. Anal., 52 (1973), 181-192.
doi: 10.1007/BF00282326. |
| [4] |
E. N. Dancer, Stable solutions on $\mathbb R^n$ and the primary branch of some non-self-adjoint convex problems, Differential Integral Equations, 17 (2004), 961-970. |
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E. N. Dancer, Finite Morse index solutions of exponential problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 173-179. |
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E. N. Dancer, Finite Morse index solutions of supercritical problems, J. Reine Angew. Math., 620 (2008), 213-233.
doi: 10.1515/CRELLE.2008.055. |
| [7] |
E. N. Dancer, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Differential Equations, 37 (1980), 404-437.
doi: 10.1016/0022-0396(80)90107-2. |
| [8] |
E. N. Dancer, Real analyticity and non-degeneracy, Math. Ann., 325 (2003), 369-392. |
| [9] |
E. N. Dancer, Stable and finite Morse index solutions on $\mathbf R^n$ or on bounded domains with small diffusion, Trans. Amer. Math. Soc., 357 (2005), 1225-1243.
doi: 10.1090/S0002-9947-04-03543-3. |
| [10] |
E. N. Dancer, Infinitely many turning points for some supercritical problems, Ann. Mat. Pura Appl. (4), 178 (2000), 225-233.
doi: 10.1007/BF02505896. |
| [11] |
E. N. Dancer and A. Farina, On the classification of solutions of $-\Delta u=e^u$ on $\mathbb R^N$: stability outside a compact set and applications, Proc. Amer. Math. Soc., 137 (2009), 1333-1338.
doi: 10.1090/S0002-9939-08-09772-4. |
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D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 1981. |
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G. Whyburn, "Topological Analysis," Princeton University Press, Princeton, N. J., 1958. |
show all references
References:
| [1] |
K. C. Chang, "Infinite-dimensional Morse Theory and Multiple Solution Problems," Birkhäuser Boston Inc., Boston, 1993. |
| [2] |
E. N. Dancer, Global structure of the solutions of non-linear real analytic eigenvalue problems, Proc. London Math. Soc., s3-27 (1973), 747-765.
doi: 10.1112/plms/s3-27.4.747. |
| [3] |
E. N. Dancer, Global solution branches for positive mappings, Arch. Rational Mech. Anal., 52 (1973), 181-192.
doi: 10.1007/BF00282326. |
| [4] |
E. N. Dancer, Stable solutions on $\mathbb R^n$ and the primary branch of some non-self-adjoint convex problems, Differential Integral Equations, 17 (2004), 961-970. |
| [5] |
E. N. Dancer, Finite Morse index solutions of exponential problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 173-179. |
| [6] |
E. N. Dancer, Finite Morse index solutions of supercritical problems, J. Reine Angew. Math., 620 (2008), 213-233.
doi: 10.1515/CRELLE.2008.055. |
| [7] |
E. N. Dancer, On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Differential Equations, 37 (1980), 404-437.
doi: 10.1016/0022-0396(80)90107-2. |
| [8] |
E. N. Dancer, Real analyticity and non-degeneracy, Math. Ann., 325 (2003), 369-392. |
| [9] |
E. N. Dancer, Stable and finite Morse index solutions on $\mathbf R^n$ or on bounded domains with small diffusion, Trans. Amer. Math. Soc., 357 (2005), 1225-1243.
doi: 10.1090/S0002-9947-04-03543-3. |
| [10] |
E. N. Dancer, Infinitely many turning points for some supercritical problems, Ann. Mat. Pura Appl. (4), 178 (2000), 225-233.
doi: 10.1007/BF02505896. |
| [11] |
E. N. Dancer and A. Farina, On the classification of solutions of $-\Delta u=e^u$ on $\mathbb R^N$: stability outside a compact set and applications, Proc. Amer. Math. Soc., 137 (2009), 1333-1338.
doi: 10.1090/S0002-9939-08-09772-4. |
| [12] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, Berlin, 1981. |
| [13] |
G. Whyburn, "Topological Analysis," Princeton University Press, Princeton, N. J., 1958. |
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