In this paper we study the global bifurcation of sign-changing radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions.
Citation: Ruyun Ma, Dongliang Yan, Liping Wei. Global bifurcation of sign-changing radial solutions of elliptic equations of order 2m in annular domains[J]. AIMS Mathematics, 2020, 5(5): 4909-4916. doi: 10.3934/math.2020313
[1] | Boris P. Andreianov, Carlotta Donadello, Ulrich Razafison, Julien Y. Rolland, Massimiliano D. Rosini . Solutions of the Aw-Rascle-Zhang system with point constraints. Networks and Heterogeneous Media, 2016, 11(1): 29-47. doi: 10.3934/nhm.2016.11.29 |
[2] | Shimao Fan, Michael Herty, Benjamin Seibold . Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model. Networks and Heterogeneous Media, 2014, 9(2): 239-268. doi: 10.3934/nhm.2014.9.239 |
[3] | Benjamin Seibold, Morris R. Flynn, Aslan R. Kasimov, Rodolfo R. Rosales . Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models. Networks and Heterogeneous Media, 2013, 8(3): 745-772. doi: 10.3934/nhm.2013.8.745 |
[4] | Michael Burger, Simone Göttlich, Thomas Jung . Derivation of second order traffic flow models with time delays. Networks and Heterogeneous Media, 2019, 14(2): 265-288. doi: 10.3934/nhm.2019011 |
[5] | Mauro Garavello . A review of conservation laws on networks. Networks and Heterogeneous Media, 2010, 5(3): 565-581. doi: 10.3934/nhm.2010.5.565 |
[6] | Bertrand Haut, Georges Bastin . A second order model of road junctions in fluid models of traffic networks. Networks and Heterogeneous Media, 2007, 2(2): 227-253. doi: 10.3934/nhm.2007.2.227 |
[7] | Michael Herty, S. Moutari, M. Rascle . Optimization criteria for modelling intersections of vehicular traffic flow. Networks and Heterogeneous Media, 2006, 1(2): 275-294. doi: 10.3934/nhm.2006.1.275 |
[8] | Michael Herty, Lorenzo Pareschi, Mohammed Seaïd . Enskog-like discrete velocity models for vehicular traffic flow. Networks and Heterogeneous Media, 2007, 2(3): 481-496. doi: 10.3934/nhm.2007.2.481 |
[9] | Cécile Appert-Rolland, Pierre Degond, Sébastien Motsch . Two-way multi-lane traffic model for pedestrians in corridors. Networks and Heterogeneous Media, 2011, 6(3): 351-381. doi: 10.3934/nhm.2011.6.351 |
[10] | Oliver Kolb, Simone Göttlich, Paola Goatin . Capacity drop and traffic control for a second order traffic model. Networks and Heterogeneous Media, 2017, 12(4): 663-681. doi: 10.3934/nhm.2017027 |
In this paper we study the global bifurcation of sign-changing radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions.
[1] |
C. V. Coffman, M. Marcus, Existence and uniqueness results for semilinear Dirichlet problems in annuli, Arch. Rational Mech. Anal., 108 (1989), 293-307. doi: 10.1007/BF01041066
![]() |
[2] |
L. H. Erbe, H. Wang, On the existence of positive solutions of ordinary di fferential equations, Proc. Amer. Math. Soc., 120 (1994), 743-748. doi: 10.1090/S0002-9939-1994-1204373-9
![]() |
[3] |
L. H. Erbe, S. C. Hu, H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl., 184 (1994), 640-648. doi: 10.1006/jmaa.1994.1227
![]() |
[4] |
K. Lan, J. R. L. Webb, Positive solutions of semilinear di fferential equations with singularities, J. Differential Equations, 148 (1998), 407-421. doi: 10.1006/jdeq.1998.3475
![]() |
[5] |
S. S. Lin, F. M. Pai, Existence and multiplicity of positive radial solutions for semilinear elliptic equations in annular domains, Siam J. Math. Anal., 22 (1991), 1500-1515. doi: 10.1137/0522097
![]() |
[6] |
H. Wang, On the existence of positive solutions for semilinear elliptic equations in the annulus, J. Differential Equations, 109 (1994), 1-7. doi: 10.1006/jdeq.1994.1042
![]() |
[7] | R. Dalmasso, Elliptic equations of order 2m in annular domains, Trans. Amer. Math. Soc., 347 (1995), 3575-3585. |
[8] |
R. Ma, B. Thompson, Nodal solutions for nonlinear eigenvalue problems, Nonlinear Anal., 59 (2004), 707-718. doi: 10.1016/j.na.2004.07.030
![]() |
[9] | E. N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J., 23 (1973/74), 1069-1076. |
[10] | U. Elias, Eigenvalue problems for the equation Ly + λp(x)y = 0, J. Differential Equations, 29 (1978), 28-57. |
[11] |
B. P. Rynne, Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems, J. Differential Equations, 188 (2003), 461-472. doi: 10.1016/S0022-0396(02)00146-8
![]() |
[12] | M. A. Naimark, Elementary theory of linear di fferential operators, New York: Ungar, 1967. |
[13] | W. A. Coppel, Disconjugacy, Lectures Notes in Math, New York: Springer-Verlag, 1971. |
[14] | U. Elias, Oscillation Theory of Two-Term Di fferential Equations, Mathematics and Its Applications, The Netherlands, Dordrecht: Kluwer Academic Publishers, 1997. |
[15] |
P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7 (1971), 487-513. doi: 10.1016/0022-1236(71)90030-9
![]() |
[16] |
P. Drábek, G. Holubová, Positive and negative solutions of one-dimensional beam equation, Appl. Math. Lett., 51 (2016), 1-7. doi: 10.1016/j.aml.2015.06.019
![]() |
[17] |
A. Cabada, R. R. Enguiça, Positive solutions of fourth order problems with clamped beam boundary conditions, Nonlinear Anal., 74 (2011), 3112-3122. doi: 10.1016/j.na.2011.01.027
![]() |
[18] |
R. Ma, H. Wang, M. Elsanosi, Spectrum of a linear fourth-order di fferential operator and its applications, Math. Nachr., 286 (2013), 1805-1819. doi: 10.1002/mana.201200288
![]() |
1. | Mohamed Benyahia, Massimiliano D. Rosini, A macroscopic traffic model with phase transitions and local point constraints on the flow, 2017, 12, 1556-181X, 297, 10.3934/nhm.2017013 | |
2. | Mohamed Benyahia, Massimiliano D. Rosini, Lack of BV bounds for approximate solutions to a two‐phase transition model arising from vehicular traffic, 2020, 43, 0170-4214, 10381, 10.1002/mma.6304 | |
3. | Mohamed Benyahia, Massimiliano D. Rosini, Entropy solutions for a traffic model with phase transitions, 2016, 141, 0362546X, 167, 10.1016/j.na.2016.04.011 | |
4. | Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini, Giovanni Russo, 2018, Chapter 37, 978-3-319-91544-9, 487, 10.1007/978-3-319-91545-6_37 | |
5. | Shuai Fan, Yu Zhang, Riemann problem and wave interactions for an inhomogeneous Aw-Rascle traffic flow model with extended Chaplygin gas, 2023, 152, 00207462, 104384, 10.1016/j.ijnonlinmec.2023.104384 | |
6. | Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini, Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux, 2018, 116, 00217824, 309, 10.1016/j.matpur.2018.01.005 | |
7. | Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini, Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic, 2017, 14, 1551-0018, 127, 10.3934/mbe.2017009 | |
8. | M. Di Francesco, S. Fagioli, M. D. Rosini, G. Russo, 2017, Chapter 9, 978-3-319-49994-9, 333, 10.1007/978-3-319-49996-3_9 | |
9. | Mohamed Benyahia, Carlotta Donadello, Nikodem Dymski, Massimiliano D. Rosini, An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic, 2018, 25, 1021-9722, 10.1007/s00030-018-0539-1 | |
10. | Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano Daniele Rosini, 2018, Chapter 5, 978-3-030-05128-0, 103, 10.1007/978-3-030-05129-7_5 | |
11. | E. Dal Santo, M. D. Rosini, N. Dymski, M. Benyahia, General phase transition models for vehicular traffic with point constraints on the flow, 2017, 40, 01704214, 6623, 10.1002/mma.4478 | |
12. | Stefano Villa, Paola Goatin, Christophe Chalons, Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model, 2017, 22, 1553-524X, 3921, 10.3934/dcdsb.2017202 | |
13. | Muhammed Ali Mehmood, Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset function, 2024, 533, 0022247X, 128028, 10.1016/j.jmaa.2023.128028 | |
14. | Wenjie Zhu, Rongyong Zhao, Hao Zhang, Cuiling Li, Ping Jia, Yunlong Ma, Dong Wang, Miyuan Li, Panic-Pressure Conversion Model From Microscopic Pedestrian Movement to Macroscopic Crowd Flow, 2023, 18, 1555-1415, 10.1115/1.4063505 | |
15. | Cecile Appert-Rolland, Alethea B.T. Barbaro, 2025, 25430009, 10.1016/bs.atpp.2025.04.004 | |
16. | Nicola De Nitti, Denis Serre, Enrique Zuazua, Pointwise constraints for scalar conservation laws with positive wave velocity, 2025, 76, 0044-2275, 10.1007/s00033-025-02459-0 |