American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 662-671. doi: 10.3934/proc.2005.2005.662

Existence and location result for a fourth order boundary value problem

Feliz Minhós 1, , T. Gyulov 2, and  A. I. Santos 1,

1. 

Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMA-UE), Rua Romão Ramalho, 59. 7000-671 Évora, Portugal, Portugal
2. 

C.A.M.I., University of Rousse, 8, "Studenska" Str., 7017 Rousse, Bulgaria

Received  August 2004 Revised  March 2005 Published  September 2005

In the present work we prove an existence and location result for the fourth order fully nonlinear equation% \begin{equation*} u^{(iv)}=f\left( t,u,u^{\prime },u^{\prime \prime },u^{\prime \prime \prime }\right) ,\quad 0
Keywords: a priori estimate, degree theory., Fourth order boundary value problem, a pair of lower and upper solutions, Nagumo condition.
Mathematics Subject Classification: 34B1.
Citation: Feliz Minhós, T. Gyulov, A. I. Santos. Existence and location result for a fourth order boundary value problem. Conference Publications, 2005, 2005 (Special) : 662-671. doi: 10.3934/proc.2005.2005.662
[1]

Alberto Cabada, João Fialho, Feliz Minhós. Non ordered lower and upper solutions to fourth order problems with functional boundary conditions. Conference Publications, 2011, 2011 (Special) : 209-218. doi: 10.3934/proc.2011.2011.209
[2]

John R. Graef, Lingju Kong, Min Wang. Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Conference Publications, 2013, 2013 (special) : 291-299. doi: 10.3934/proc.2013.2013.291
[3]

John R. Graef, Johnny Henderson, Bo Yang. Positive solutions to a fourth order three point boundary value problem. Conference Publications, 2009, 2009 (Special) : 269-275. doi: 10.3934/proc.2009.2009.269
[4]

Zhilin Yang, Jingxian Sun. Positive solutions of a fourth-order boundary value problem involving derivatives of all orders. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1615-1628. doi: 10.3934/cpaa.2012.11.1615
[5]

Wenxiong Chen, Congming Li. A priori estimate for the Nirenberg problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 225-233. doi: 10.3934/dcdss.2008.1.225
[6]

Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615
[7]

Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5217-5226. doi: 10.3934/dcdsb.2020340
[8]

Boling Guo, Jun Wu. Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3749-3778. doi: 10.3934/dcdsb.2021205
[9]

Alberto Boscaggin, Fabio Zanolin. Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 89-110. doi: 10.3934/dcds.2013.33.89
[10]

John R. Graef, Lingju Kong, Bo Yang. Positive solutions of a nonlinear higher order boundary-value problem. Conference Publications, 2009, 2009 (Special) : 276-285. doi: 10.3934/proc.2009.2009.276
[11]

John R. Graef, Bo Yang. Multiple positive solutions to a three point third order boundary value problem. Conference Publications, 2005, 2005 (Special) : 337-344. doi: 10.3934/proc.2005.2005.337
[12]

John R. Graef, Bo Yang. Positive solutions of a third order nonlocal boundary value problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 89-97. doi: 10.3934/dcdss.2008.1.89
[13]

Xu Liu, Jun Zhou. Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity. Electronic Research Archive, 2020, 28 (2) : 599-625. doi: 10.3934/era.2020032
[14]

Rubén Figueroa, Rodrigo López Pouso, Jorge Rodríguez–López. Existence and multiplicity results for second-order discontinuous problems via non-ordered lower and upper solutions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 617-633. doi: 10.3934/dcdsb.2019257
[15]

Chunyan Ji, Yang Xue, Yong Li. Periodic solutions for SDEs through upper and lower solutions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4737-4754. doi: 10.3934/dcdsb.2020122
[16]

João Fialho, Feliz Minhós. The role of lower and upper solutions in the generalization of Lidstone problems. Conference Publications, 2013, 2013 (special) : 217-226. doi: 10.3934/proc.2013.2013.217
[17]

Luisa Malaguti, Cristina Marcelli. Existence of bounded trajectories via upper and lower solutions. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 575-590. doi: 10.3934/dcds.2000.6.575
[18]

Massimo Tarallo, Zhe Zhou. Limit periodic upper and lower solutions in a generic sense. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 293-309. doi: 10.3934/dcds.2018014
[19]

Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla. Positive radial solutions of a nonlinear boundary value problem. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1765-1783. doi: 10.3934/cpaa.2018084
[20]

Tokushi Sato, Tatsuya Watanabe. Singular positive solutions for a fourth order elliptic problem in $R$. Communications on Pure and Applied Analysis, 2011, 10 (1) : 245-268. doi: 10.3934/cpaa.2011.10.245

 Impact Factor: 

Tools

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy