A Note on Some Nonlinear Fourth Order Differential Equations
Bollettino dell'Unione Matematica Italiana (2013)
- Volume: 6, Issue: 2, page 349-361
- ISSN: 0392-4041
Access Full Article
topAbstract
topHow to cite
topBerchio, Elvise. "A Note on Some Nonlinear Fourth Order Differential Equations." Bollettino dell'Unione Matematica Italiana 6.2 (2013): 349-361. <http://eudml.org/doc/294050>.
@article{Berchio2013,
abstract = {For a family of fourth order semilinear ordinary differential equations we discuss some fundamental issues, such as global continuation of solutions and their qualitative behavior. The note is the summary of a communication given at the XIX Congress of U.M.I. (Bologna - September 12-17, 2011).},
author = {Berchio, Elvise},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {349-361},
publisher = {Unione Matematica Italiana},
title = {A Note on Some Nonlinear Fourth Order Differential Equations},
url = {http://eudml.org/doc/294050},
volume = {6},
year = {2013},
}
TY - JOUR
AU - Berchio, Elvise
TI - A Note on Some Nonlinear Fourth Order Differential Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/6//
PB - Unione Matematica Italiana
VL - 6
IS - 2
SP - 349
EP - 361
AB - For a family of fourth order semilinear ordinary differential equations we discuss some fundamental issues, such as global continuation of solutions and their qualitative behavior. The note is the summary of a communication given at the XIX Congress of U.M.I. (Bologna - September 12-17, 2011).
LA - eng
UR - http://eudml.org/doc/294050
ER -
References
top- ARIOLI, G. - GAZZOLA, F. - GRUNAU, H.-CH., Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity, J. Diff. Eq.230 (2006), 743-770. Zbl1152.35360MR2269942DOI10.1016/j.jde.2006.05.015
- ARIOLI, G. - GAZZOLA, F. - GRUNAU, H.-CH. - MITIDIERI, E., A semilinear fourth order elliptic problem with exponential nonlinearity, SIAM J. Math. Anal.36, (2005), 1226-1258. Zbl1162.35339MR2139208DOI10.1137/S0036141002418534
- BERCHIO, E. - CASSANI, D. - GAZZOLA, F., Hardy-Rellich inequalities with boundary remainder terms and applications, Manuscripta Math.131 (2010), 427-458. Zbl1187.35045MR2592089DOI10.1007/s00229-009-0328-6
- BERCHIO, E. - FARINA, A. - FERRERO, A. - GAZZOLA, F., Existence and stability of entire solutions to a semilinear fourth order elliptic problem, J. Diff. Eq.252 (2012), 2596-2616. Zbl1235.35126MR2860632DOI10.1016/j.jde.2011.09.028
- BERCHIO, E. - FERRERO, A. - GAZZOLA, F. - KARAGEORGIS, P., Qualitative behavior of global solutions to some nonlinear fourth order differential equations, J. Diff. Eq.251 (2011), 2696-2727. Zbl1236.34042MR2831710DOI10.1016/j.jde.2011.05.036
- BERCHIO, E. - GAZZOLA, F., Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities, Electronic J. Diff. Eq.34 (2005), 1-20. Zbl1129.35349MR2135245
- BONHEURE, D. - SANCHEZ, L., Heteroclinic orbits for some classes of second and fourth order differential equations, Handbook of Diff. Eq. Vol. III, Elsevier Science (2006), 103-202. MR2457633DOI10.1016/S1874-5725(06)80006-4
- BREUER, B. - HÓRAK, J. - MCKENNA, P. J. - PLUM, M., A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam, J. Diff. Eq.224 (2006), 60-97. Zbl1104.34034MR2220064DOI10.1016/j.jde.2005.07.016
- CHANG, S. Y. A. - CHEN, W., A note on a class of higher order conformally covariant equations, Discrete Cont. Dyn. Syst.7 (2001), 275-281. Zbl1014.35025MR1808400DOI10.3934/dcds.2001.7.275
- CHEN, Y. - MCKENNA, P. J., Traveling waves in a nonlinearly suspended beam: theoretical results and numerical observations, J. Diff. Eq.136 (1997), 325-355. Zbl0879.35113MR1448828DOI10.1006/jdeq.1996.3155
- DÁVILA, J. - DUPAIGNE, L. - GUERRA, I. - MONTENEGRO, M., Stable solutions for the bilaplacian with exponential nonlinearity, SIAM J. Math. Anal.39 (2007), 565-592. Zbl1138.35022MR2338421DOI10.1137/060665579
- DÁVILA, J. - FLORES, I. - GUERRA, I., Multiplicity of solutions for a fourth order problem with exponential nonlinearity, J. Diff. Eq.247 (2009), 3136-3162. Zbl1190.34017MR2569861DOI10.1016/j.jde.2009.07.023
- GAZZOLA, F. - PAVANI, R., Blow up oscillating solutions to some nonlinear fourth order differential equations, Nonlin. Anal. TMA74 (2011), 6696-6711. Zbl1237.34043MR2834070DOI10.1016/j.na.2011.06.049
- GAZZOLA, F. - PAVANI, R., Blow-up oscillating solutions to some nonlinear fourth order differential equations describing oscillations of suspension bridges, IAB- MAS12, 6th International Conference on Bridge Maintenance, Safety, Management, Resilience and Sustainability, Stresa 2012, Biondini- Frangopol (Editors), Taylor-Francis Group (London, 2001), 3089-3093.
- GEL'FAND, I. M., Some problems in the theory of quasilinear equations, Section 15, due to G. I. Barenblatt, Amer. Math. Soc. Transl. II. Ser. 29 (1963), 295-381. Russian original: Uspekhi Mat. Nauk.14 (1959), 87-158. MR110868
- JOSEPH, D. - LUNDGREN, T. S., Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal.49 (1973), 241-269. Zbl0266.34021MR340701DOI10.1007/BF00250508
- KARAGEORGIS, P. - MCKENNA, P. J., The existence of ground states for fourth-order wave equations, Nonlinear Analysis73 (2010), 367-373. Zbl1192.35113MR2650820DOI10.1016/j.na.2010.03.025
- KARAGEORGIS, P. - STALKER, J. G., A lower bound for the amplitude of traveling waves of suspension bridges, Nonlinear Analysis75 (2012), 5212-5214. Zbl1266.34078MR2927583DOI10.1016/j.na.2012.04.037
- LIN, C. S., A classification of solutions of a conformally invariant fourth order equation in , Comment. Math. Helv.73 (1998), 206-231. Zbl0933.35057MR1611691DOI10.1007/s000140050052
- MCKENNA, P. J. - WALTER, W., Traveling waves in a suspension bridge, SIAM J. Appl. Math.50 (1990), 703-715. Zbl0699.73038MR1050908DOI10.1137/0150041
- MCKENNA, P. J., Large-amplitude periodic oscillations in simple and complex mechanical systems: outgrowths from nonlinear analysis, Milan J. Math.74 (2006), 79-115. Zbl1117.35025MR2278730DOI10.1007/s00032-006-0052-6
- PELETIER, L. A. - TROY, W. C., Spatial patterns. Higher order models in physics and mechanics. Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Boston Inc., Boston, MA 45 (2001). Zbl1076.34515MR1839555DOI10.1007/978-1-4612-0135-9
- PELETIER, M. A., Sequential buckling: a variational analysis, SIAM J. Math. Anal.32 (2001), 1142-1168. Zbl1049.74023MR1828315DOI10.1137/S0036141099359925
- SMETS, D. - VAN DEN BERG, J. B., Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations, J. Diff. Eq.184 (2002), 78-96. Zbl1029.34036MR1929147DOI10.1006/jdeq.2001.4135
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.