
Previous Article
Regularization for illposed inhomogeneous evolution problems in a Hilbert space
 PROC Home
 This Issue

Next Article
Positive solutions of nonlocal fractional boundary value problems
Existence of nontrivial solutions to systems of multipoint boundary value problems
1.  Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States 
2.  Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149 
References:
[1] 
D. Averna and G. Bonanno, A mountain pass theorem for a suitable class of functions,, {\it Rocky Mountain J. Math.} {\bf 39} (2009), 39 (2009), 707. Google Scholar 
[2] 
D. Averna and G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem,, {\it Topol. Methods Nonlinear Anal.} {\bf 22} (2003), 22 (2003), 93. Google Scholar 
[3] 
G. Bonanno, A critical point theorem via the Ekeland variational principle,, {\it Nonlinear Anal.} {\bf 75} (2012), 75 (2012), 2992. Google Scholar 
[4] 
G. Bonanno and P. Candito, Nondifferentiable functionals and applications to elliptic problems with discontinuous nonlinearities,, {\it J. Differential Equations} {\bf 244} (2008), 244 (2008), 3031. Google Scholar 
[5] 
Z. Du and L. Kong, Existence of three solutions for systems of multipoint boundary value problems,, {\it Electron. J. Qual. Theory Diff. Equ.}, (2009). Google Scholar 
[6] 
P. W. Eloe and B. Ahmad, Positive solutions of a nonlinear $n$th order boundary value problem with nonlocal conditions,, {\it Appl. Math. Lett.} {\bf 18} (2005), 18 (2005), 521. Google Scholar 
[7] 
H. Feng and W. Ge, Existence of three positive solutions for $M$point boundaryvalue problem with onedimensional,, {\it Taiwanese J. Math.} {\bf 14} (2010), 14 (2010), 647. Google Scholar 
[8] 
W. Feng and J. R. L. Webb, Solvability of $m$point boundary value problems with nonlinear growth,, {\it J. Math. Anal. Appl.} {\bf 212} (1997), 212 (1997), 467. Google Scholar 
[9] 
J. R. Graef, S. Heidarkhani, and L. Kong, A critical points approach to multiplicity results for multipoint boundary value problems,, {\it Appl. Anal.} {\bf 90} (2011), 90 (2011), 1909. Google Scholar 
[10] 
J. R. Graef, S. Heidarkhani, and L. Kong, Infinitely many solutions for systems of multipoint boundary value problems using variational methods,, {\it Topol. Methods Nonlinear Anal.} {\bf 42} (2013), 42 (2013), 105. Google Scholar 
[11] 
J. R. Graef, L. Kong, Existence of solutions for nonlinear boundary value problems,, {\it Comm. Appl. Nonlinear Anal.} {\bf 14} (2007), 14 (2007), 39. Google Scholar 
[12] 
J. R. Graef, L. Kong, Q. Kong, Higher order multipoint boundary value problems,, {\it Math. Nachr.} {\bf 284} (2011), 284 (2011), 39. Google Scholar 
[13] 
S. Heidarkhani, Multiple solutions for a class of multipoint boundary value systems driven by a one dimensional ($p_1,\ldots, p_n$)Laplacian operator,, {\it Abstract Appl. Anal.} {\bf 2012} (2012), 2012 (2012). Google Scholar 
[14] 
J. Henderson, Solutions of multipoint boundary value problems for second order equations,, {\it Dynam. Syst. Appl.} {\bf 15} (2006), 15 (2006), 111. Google Scholar 
[15] 
J. Henderson, B. Karna, and C. C. Tisdell, Existence of solutions for threepoint boundary value problems for second order equations,, {\it Proc. Amer. Math. Soc.} {\bf 133} (2005), 133 (2005), 1365. Google Scholar 
[16] 
J. Henderson and S. K. Ntouyas, Positive solutions for systems of $n$th order threepoint nonlocal boundary value problems,, {\it Electron. J. Qual. Theory Diff. Equ.} 2007, (2007). Google Scholar 
[17] 
D. Ma and X. Chen, Existence and iteration of positive solutions for a multipoint boundary value problem with a $p$Laplacian operator,, {\it Portugal. Math. (N. S.)} {\bf 65} (2008), 65 (2008), 67. Google Scholar 
[18] 
R. Ma, Existence of positive solutions for superlinear $m$point boundary value problems,, {\it Proc. Edinburgh Math. Soc.} {\bf 46} (2003), 46 (2003), 279. Google Scholar 
[19] 
R. Ma and D. O'Regan, Solvability of singular second order $m$point boundary value problems,, {\it J. Math. Anal. Appl.} {\bf 301} (2005), 301 (2005), 124. Google Scholar 
[20] 
B. Ricceri, A general variational principle and some of its applications,, {\it J. Comput. Appl. Math.} {\bf 113} (2000), 113 (2000), 401. Google Scholar 
[21] 
E. Zeidler, Nonlinear functional analysis and its applications,, Vol. II., (1985). Google Scholar 
show all references
References:
[1] 
D. Averna and G. Bonanno, A mountain pass theorem for a suitable class of functions,, {\it Rocky Mountain J. Math.} {\bf 39} (2009), 39 (2009), 707. Google Scholar 
[2] 
D. Averna and G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem,, {\it Topol. Methods Nonlinear Anal.} {\bf 22} (2003), 22 (2003), 93. Google Scholar 
[3] 
G. Bonanno, A critical point theorem via the Ekeland variational principle,, {\it Nonlinear Anal.} {\bf 75} (2012), 75 (2012), 2992. Google Scholar 
[4] 
G. Bonanno and P. Candito, Nondifferentiable functionals and applications to elliptic problems with discontinuous nonlinearities,, {\it J. Differential Equations} {\bf 244} (2008), 244 (2008), 3031. Google Scholar 
[5] 
Z. Du and L. Kong, Existence of three solutions for systems of multipoint boundary value problems,, {\it Electron. J. Qual. Theory Diff. Equ.}, (2009). Google Scholar 
[6] 
P. W. Eloe and B. Ahmad, Positive solutions of a nonlinear $n$th order boundary value problem with nonlocal conditions,, {\it Appl. Math. Lett.} {\bf 18} (2005), 18 (2005), 521. Google Scholar 
[7] 
H. Feng and W. Ge, Existence of three positive solutions for $M$point boundaryvalue problem with onedimensional,, {\it Taiwanese J. Math.} {\bf 14} (2010), 14 (2010), 647. Google Scholar 
[8] 
W. Feng and J. R. L. Webb, Solvability of $m$point boundary value problems with nonlinear growth,, {\it J. Math. Anal. Appl.} {\bf 212} (1997), 212 (1997), 467. Google Scholar 
[9] 
J. R. Graef, S. Heidarkhani, and L. Kong, A critical points approach to multiplicity results for multipoint boundary value problems,, {\it Appl. Anal.} {\bf 90} (2011), 90 (2011), 1909. Google Scholar 
[10] 
J. R. Graef, S. Heidarkhani, and L. Kong, Infinitely many solutions for systems of multipoint boundary value problems using variational methods,, {\it Topol. Methods Nonlinear Anal.} {\bf 42} (2013), 42 (2013), 105. Google Scholar 
[11] 
J. R. Graef, L. Kong, Existence of solutions for nonlinear boundary value problems,, {\it Comm. Appl. Nonlinear Anal.} {\bf 14} (2007), 14 (2007), 39. Google Scholar 
[12] 
J. R. Graef, L. Kong, Q. Kong, Higher order multipoint boundary value problems,, {\it Math. Nachr.} {\bf 284} (2011), 284 (2011), 39. Google Scholar 
[13] 
S. Heidarkhani, Multiple solutions for a class of multipoint boundary value systems driven by a one dimensional ($p_1,\ldots, p_n$)Laplacian operator,, {\it Abstract Appl. Anal.} {\bf 2012} (2012), 2012 (2012). Google Scholar 
[14] 
J. Henderson, Solutions of multipoint boundary value problems for second order equations,, {\it Dynam. Syst. Appl.} {\bf 15} (2006), 15 (2006), 111. Google Scholar 
[15] 
J. Henderson, B. Karna, and C. C. Tisdell, Existence of solutions for threepoint boundary value problems for second order equations,, {\it Proc. Amer. Math. Soc.} {\bf 133} (2005), 133 (2005), 1365. Google Scholar 
[16] 
J. Henderson and S. K. Ntouyas, Positive solutions for systems of $n$th order threepoint nonlocal boundary value problems,, {\it Electron. J. Qual. Theory Diff. Equ.} 2007, (2007). Google Scholar 
[17] 
D. Ma and X. Chen, Existence and iteration of positive solutions for a multipoint boundary value problem with a $p$Laplacian operator,, {\it Portugal. Math. (N. S.)} {\bf 65} (2008), 65 (2008), 67. Google Scholar 
[18] 
R. Ma, Existence of positive solutions for superlinear $m$point boundary value problems,, {\it Proc. Edinburgh Math. Soc.} {\bf 46} (2003), 46 (2003), 279. Google Scholar 
[19] 
R. Ma and D. O'Regan, Solvability of singular second order $m$point boundary value problems,, {\it J. Math. Anal. Appl.} {\bf 301} (2005), 301 (2005), 124. Google Scholar 
[20] 
B. Ricceri, A general variational principle and some of its applications,, {\it J. Comput. Appl. Math.} {\bf 113} (2000), 113 (2000), 401. Google Scholar 
[21] 
E. Zeidler, Nonlinear functional analysis and its applications,, Vol. II., (1985). Google Scholar 
[1] 
Lingju Kong, Qingkai Kong. Existence of nodal solutions of multipoint boundary value problems. Conference Publications, 2009, 2009 (Special) : 457465. doi: 10.3934/proc.2009.2009.457 
[2] 
Yu Tian, John R. Graef, Lingju Kong, Min Wang. Existence of solutions to a multipoint boundary value problem for a second order differential system via the dual least action principle. Conference Publications, 2013, 2013 (special) : 759769. doi: 10.3934/proc.2013.2013.759 
[3] 
Marta GarcíaHuidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313319. doi: 10.3934/proc.2003.2003.313 
[4] 
ShaoYuan Huang, ShinHwa Wang. On Sshaped bifurcation curves for a twopoint boundary value problem arising in a theory of thermal explosion. Discrete & Continuous Dynamical Systems  A, 2015, 35 (10) : 48394858. doi: 10.3934/dcds.2015.35.4839 
[5] 
Djédjé Sylvain Zézé, Michel PotierFerry, Yannick Tampango. Multipoint Taylor series to solve differential equations. Discrete & Continuous Dynamical Systems  S, 2019, 12 (6) : 17911806. doi: 10.3934/dcdss.2019118 
[6] 
ChanGyun Kim, YongHoon Lee. A bifurcation result for two point boundary value problem with a strong singularity. Conference Publications, 2011, 2011 (Special) : 834843. doi: 10.3934/proc.2011.2011.834 
[7] 
John R. Graef, Bo Yang. Multiple positive solutions to a three point third order boundary value problem. Conference Publications, 2005, 2005 (Special) : 337344. doi: 10.3934/proc.2005.2005.337 
[8] 
Wenming Zou. Multiple solutions results for twopoint boundary value problem with resonance. Discrete & Continuous Dynamical Systems  A, 1998, 4 (3) : 485496. doi: 10.3934/dcds.1998.4.485 
[9] 
John R. Graef, Johnny Henderson, Bo Yang. Positive solutions to a fourth order three point boundary value problem. Conference Publications, 2009, 2009 (Special) : 269275. doi: 10.3934/proc.2009.2009.269 
[10] 
Jingxian Sun, Shouchuan Hu. Flowinvariant sets and critical point theory. Discrete & Continuous Dynamical Systems  A, 2003, 9 (2) : 483496. doi: 10.3934/dcds.2003.9.483 
[11] 
Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 7278. doi: 10.3934/proc.1998.1998.72 
[12] 
Martin Oberlack, Andreas Rosteck. New statistical symmetries of the multipoint equations and its importance for turbulent scaling laws. Discrete & Continuous Dynamical Systems  S, 2010, 3 (3) : 451471. doi: 10.3934/dcdss.2010.3.451 
[13] 
K. Q. Lan, G. C. Yang. Optimal constants for two point boundary value problems. Conference Publications, 2007, 2007 (Special) : 624633. doi: 10.3934/proc.2007.2007.624 
[14] 
Jeffrey W. Lyons. An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem. Conference Publications, 2015, 2015 (special) : 775782. doi: 10.3934/proc.2015.0775 
[15] 
Salvatore A. Marano, Sunra Mosconi. Nonsmooth critical point theory on closed convex sets. Communications on Pure & Applied Analysis, 2014, 13 (3) : 11871202. doi: 10.3934/cpaa.2014.13.1187 
[16] 
J. R. L. Webb. Remarks on positive solutions of some three point boundary value problems. Conference Publications, 2003, 2003 (Special) : 905915. doi: 10.3934/proc.2003.2003.905 
[17] 
K. Q. Lan. Properties of kernels and eigenvalues for three point boundary value problems. Conference Publications, 2005, 2005 (Special) : 546555. doi: 10.3934/proc.2005.2005.546 
[18] 
Wenying Feng. Solutions and positive solutions for some threepoint boundary value problems. Conference Publications, 2003, 2003 (Special) : 263272. doi: 10.3934/proc.2003.2003.263 
[19] 
Feliz Minhós, A. I. Santos. Higher order twopoint boundary value problems with asymmetric growth. Discrete & Continuous Dynamical Systems  S, 2008, 1 (1) : 127137. doi: 10.3934/dcdss.2008.1.127 
[20] 
Marek Rychlik. The Equichordal Point Problem. Electronic Research Announcements, 1996, 2: 108123. 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]