2009, 2009(Special): 457-465. doi: 10.3934/proc.2009.2009.457

Existence of nodal solutions of multi-point boundary value problems

1. 

Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403

2. 

Department of Mathematics, Northern Illinois University, DeKalb, Il 60115, United States

Received  July 2008 Revised  March 2009 Published  September 2009

We study the nonlinear boundary value problem consisting of the equation $y^{''}+ w(t)f(y)=0$ on $[a,b]$ and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes of the existence of different types of nodal solutions as the problem changes.
Citation: Lingju Kong, Qingkai Kong. Existence of nodal solutions of multi-point boundary value problems. Conference Publications, 2009, 2009 (Special) : 457-465. doi: 10.3934/proc.2009.2009.457
[1]

John R. Graef, Shapour Heidarkhani, Lingju Kong. Existence of nontrivial solutions to systems of multi-point boundary value problems. Conference Publications, 2013, 2013 (special) : 273-281. doi: 10.3934/proc.2013.2013.273

[2]

Guglielmo Feltrin. Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 1083-1102. doi: 10.3934/cpaa.2017052

[3]

K. Q. Lan. Properties of kernels and eigenvalues for three point boundary value problems. Conference Publications, 2005, 2005 (Special) : 546-555. doi: 10.3934/proc.2005.2005.546

[4]

Russell Johnson, Luca Zampogni. On the inverse Sturm-Liouville problem. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 405-428. doi: 10.3934/dcds.2007.18.405

[5]

Yu Tian, John R. Graef, Lingju Kong, Min Wang. Existence of solutions to a multi-point boundary value problem for a second order differential system via the dual least action principle. Conference Publications, 2013, 2013 (special) : 759-769. doi: 10.3934/proc.2013.2013.759

[6]

Wenying Feng. Solutions and positive solutions for some three-point boundary value problems. Conference Publications, 2003, 2003 (Special) : 263-272. doi: 10.3934/proc.2003.2003.263

[7]

J. R. L. Webb. Remarks on positive solutions of some three point boundary value problems. Conference Publications, 2003, 2003 (Special) : 905-915. doi: 10.3934/proc.2003.2003.905

[8]

Elimhan N. Mahmudov. Optimization of fourth order Sturm-Liouville type differential inclusions with initial point constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2018145

[9]

N. A. Chernyavskaya, L. A. Shuster. Spaces admissible for the Sturm-Liouville equation. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1023-1052. doi: 10.3934/cpaa.2018050

[10]

K. Q. Lan, G. C. Yang. Optimal constants for two point boundary value problems. Conference Publications, 2007, 2007 (Special) : 624-633. doi: 10.3934/proc.2007.2007.624

[11]

K. Q. Lan. Multiple positive eigenvalues of conjugate boundary value problems with singularities. Conference Publications, 2003, 2003 (Special) : 501-506. doi: 10.3934/proc.2003.2003.501

[12]

Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533

[13]

Chuan-Fu Yang, Natalia Pavlovna Bondarenko. A partial inverse problem for the Sturm-Liouville operator on the lasso-graph. Inverse Problems & Imaging, 2019, 13 (1) : 69-79. doi: 10.3934/ipi.2019004

[14]

Feliz Minhós, A. I. Santos. Higher order two-point boundary value problems with asymmetric growth. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 127-137. doi: 10.3934/dcdss.2008.1.127

[15]

G. Infante. Positive solutions of nonlocal boundary value problems with singularities. Conference Publications, 2009, 2009 (Special) : 377-384. doi: 10.3934/proc.2009.2009.377

[16]

John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. Positive solutions of nonlocal fractional boundary value problems. Conference Publications, 2013, 2013 (special) : 283-290. doi: 10.3934/proc.2013.2013.283

[17]

John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83

[18]

Chuangqiang Hu, Shudi Yang. Multi-point codes from the GGS curves. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020020

[19]

Elimhan N. Mahmudov. Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019066

[20]

Grey Ballard, John Baxley, Nisrine Libbus. Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems. Communications on Pure & Applied Analysis, 2006, 5 (2) : 251-259. doi: 10.3934/cpaa.2006.5.251

 Impact Factor: 

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]