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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., (1993).
|
[2] |
E. N. Dancer, Global structure of the solutions of non-linear real analytic eigenvalue problems,, Proc. London Math. Soc., s3-27 (1973), 3.
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.
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.
|
[5] |
E. N. Dancer, Finite Morse index solutions of exponential problems,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 173.
|
[6] |
E. N. Dancer, Finite Morse index solutions of supercritical problems,, J. Reine Angew. Math., 620 (2008), 213.
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.
doi: 10.1016/0022-0396(80)90107-2. |
[8] |
E. N. Dancer, Real analyticity and non-degeneracy,, Math. Ann., 325 (2003), 369.
|
[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.
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.
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.
doi: 10.1090/S0002-9939-08-09772-4. |
[12] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Springer-Verlag, (1981).
|
[13] |
G. Whyburn, "Topological Analysis,", Princeton University Press, (1958). Google Scholar |
show all references
References:
[1] |
K. C. Chang, "Infinite-dimensional Morse Theory and Multiple Solution Problems,", Birkhäuser Boston Inc., (1993).
|
[2] |
E. N. Dancer, Global structure of the solutions of non-linear real analytic eigenvalue problems,, Proc. London Math. Soc., s3-27 (1973), 3.
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.
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.
|
[5] |
E. N. Dancer, Finite Morse index solutions of exponential problems,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 173.
|
[6] |
E. N. Dancer, Finite Morse index solutions of supercritical problems,, J. Reine Angew. Math., 620 (2008), 213.
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.
doi: 10.1016/0022-0396(80)90107-2. |
[8] |
E. N. Dancer, Real analyticity and non-degeneracy,, Math. Ann., 325 (2003), 369.
|
[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.
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.
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.
doi: 10.1090/S0002-9939-08-09772-4. |
[12] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,", Springer-Verlag, (1981).
|
[13] |
G. Whyburn, "Topological Analysis,", Princeton University Press, (1958). Google Scholar |
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