-
Previous Article
On improvement of summability properties in nonautonomous Kolmogorov equations
- CPAA Home
- This Issue
-
Next Article
Global existence and pointwise estimates of solutions for the multidimensional generalized Boussinesq-type equation
Disconjugacy and extremal solutions of nonlinear third-order equations
1. | Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China |
References:
[1] |
F. Bernis and L. A. Peleter, Two problems from draining flows involving third-order ordinary differential equation ,, \emph{SIAM J. Math. Anal.}, 27 (1996), 515.
doi: 10.1137/S0036141093260847. |
[2] |
A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems ,, \emph{J. Math. Anal. Appl.}, 185 (1994), 302.
doi: 10.1006/jmaa.1994.1250. |
[3] |
A. Cabada and R. Enguica, Positive solutions of fourth order problems with clamped beam boundary conditions ,, \emph{Nonlinear Analysis}, 74 (2011), 3112.
doi: 10.1016/j.na.2011.01.027. |
[4] |
W. A. Coppel, Disconjugacy. Lecture Notes in Mathematics, 220,, Springer-Verlag, (1971).
|
[5] |
U. Elias, Eigenvalue problems for the equations $Ly + \lambda p(x)y=0$ ,, \emph{Journal of Differential Equations}, 29 (1978), 28.
doi: 10.1016/0022-0396(78)90039-6. |
[6] |
U. Elias, Oscillation Theory of Two-Term Differential Equations (Mathematics and Its Applications), 396,, Kluwer Academic Publishers, (1997).
doi: 10.1007/978-94-017-2517-0. |
[7] |
M. Gregus, Third order linear differential equations (Mathematics and its Applications),, Reidel, (1987).
doi: 10.1007/978-94-009-3715-4. |
[8] |
L. K. Jackson, Existence and uniqueness of solutions of boundary value problems for third order differential equations ,, \emph{J. Differential Equations}, 13 (1973), 432.
doi: 10.1016/0022-0396(73)90002-8. |
[9] |
G. Klaasen, Differential inequalities and existence theorems for second and third order boundary value problems ,, \emph{J. Differential Equations}, 10 (1971), 529.
doi: 10.1016/0022-0396(71)90010-6. |
[10] |
S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem ,, \emph{J. Math. Anal. Appl.}, 323 (2006), 413.
doi: 10.1016/j.jmaa.2005.10.037. |
[11] |
R. Ma, Multiplicity results for a third order boundary value problem at resonance ,, \emph{Nonlinear Anal.}, 32 (1998), 493.
doi: 10.1016/S0362-546X(97)00494-X. |
[12] |
D. J. O'Regan, Topological transversality: Application to third-order boundary value problem ,, \emph{SIAM J. Math. Anal.}, 19 (1987), 630.
doi: 10.1137/0518048. |
[13] |
B. P. Rynne, Global bifurcation for 2$m$th-order boundary value problems and infinitely many solutions of superlinear problems ,, \emph{J. Differential Equations}, 188 (2003), 461.
doi: 10.1016/S0022-0396(02)00146-8. |
[14] |
W. C. Troy, Solution of third order differential equations relevant to draining and coating flows ,, \emph{SIAM J. Math. Anal.}, 24 (1993), 155.
doi: 10.1137/0524010. |
[15] |
Q. Yao and Y. Feng, The existence of solutions for a third order two-point boundary value problem ,, \emph{Appl. Math. Lett.}, 15 (2002), 227.
doi: 10.1016/S0893-9659(01)00122-7. |
show all references
References:
[1] |
F. Bernis and L. A. Peleter, Two problems from draining flows involving third-order ordinary differential equation ,, \emph{SIAM J. Math. Anal.}, 27 (1996), 515.
doi: 10.1137/S0036141093260847. |
[2] |
A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems ,, \emph{J. Math. Anal. Appl.}, 185 (1994), 302.
doi: 10.1006/jmaa.1994.1250. |
[3] |
A. Cabada and R. Enguica, Positive solutions of fourth order problems with clamped beam boundary conditions ,, \emph{Nonlinear Analysis}, 74 (2011), 3112.
doi: 10.1016/j.na.2011.01.027. |
[4] |
W. A. Coppel, Disconjugacy. Lecture Notes in Mathematics, 220,, Springer-Verlag, (1971).
|
[5] |
U. Elias, Eigenvalue problems for the equations $Ly + \lambda p(x)y=0$ ,, \emph{Journal of Differential Equations}, 29 (1978), 28.
doi: 10.1016/0022-0396(78)90039-6. |
[6] |
U. Elias, Oscillation Theory of Two-Term Differential Equations (Mathematics and Its Applications), 396,, Kluwer Academic Publishers, (1997).
doi: 10.1007/978-94-017-2517-0. |
[7] |
M. Gregus, Third order linear differential equations (Mathematics and its Applications),, Reidel, (1987).
doi: 10.1007/978-94-009-3715-4. |
[8] |
L. K. Jackson, Existence and uniqueness of solutions of boundary value problems for third order differential equations ,, \emph{J. Differential Equations}, 13 (1973), 432.
doi: 10.1016/0022-0396(73)90002-8. |
[9] |
G. Klaasen, Differential inequalities and existence theorems for second and third order boundary value problems ,, \emph{J. Differential Equations}, 10 (1971), 529.
doi: 10.1016/0022-0396(71)90010-6. |
[10] |
S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem ,, \emph{J. Math. Anal. Appl.}, 323 (2006), 413.
doi: 10.1016/j.jmaa.2005.10.037. |
[11] |
R. Ma, Multiplicity results for a third order boundary value problem at resonance ,, \emph{Nonlinear Anal.}, 32 (1998), 493.
doi: 10.1016/S0362-546X(97)00494-X. |
[12] |
D. J. O'Regan, Topological transversality: Application to third-order boundary value problem ,, \emph{SIAM J. Math. Anal.}, 19 (1987), 630.
doi: 10.1137/0518048. |
[13] |
B. P. Rynne, Global bifurcation for 2$m$th-order boundary value problems and infinitely many solutions of superlinear problems ,, \emph{J. Differential Equations}, 188 (2003), 461.
doi: 10.1016/S0022-0396(02)00146-8. |
[14] |
W. C. Troy, Solution of third order differential equations relevant to draining and coating flows ,, \emph{SIAM J. Math. Anal.}, 24 (1993), 155.
doi: 10.1137/0524010. |
[15] |
Q. Yao and Y. Feng, The existence of solutions for a third order two-point boundary value problem ,, \emph{Appl. Math. Lett.}, 15 (2002), 227.
doi: 10.1016/S0893-9659(01)00122-7. |
[1] |
Alberto Boscaggin, Fabio Zanolin. Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 89-110. doi: 10.3934/dcds.2013.33.89 |
[2] |
Aeeman Fatima, F. M. Mahomed, Chaudry Masood Khalique. Conditional symmetries of nonlinear third-order ordinary differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 655-666. doi: 10.3934/dcdss.2018040 |
[3] |
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 |
[4] |
John R. Graef, Bo Yang. Positive solutions of a third order nonlocal boundary value problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 89-97. doi: 10.3934/dcdss.2008.1.89 |
[5] |
Júlio Cesar Santos Sampaio, Igor Leite Freire. Symmetries and solutions of a third order equation. Conference Publications, 2015, 2015 (special) : 981-989. doi: 10.3934/proc.2015.0981 |
[6] |
Jie Shen, Li-Lian Wang. Laguerre and composite Legendre-Laguerre Dual-Petrov-Galerkin methods for third-order equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1381-1402. doi: 10.3934/dcdsb.2006.6.1381 |
[7] |
John R. Graef, Lingju Kong. Uniqueness and parameter dependence of positive solutions of third order boundary value problems with $p$-laplacian. Conference Publications, 2011, 2011 (Special) : 515-522. doi: 10.3934/proc.2011.2011.515 |
[8] |
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 |
[9] |
Massimo Tarallo, Zhe Zhou. Limit periodic upper and lower solutions in a generic sense. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 293-309. doi: 10.3934/dcds.2018014 |
[10] |
Luisa Malaguti, Cristina Marcelli. Existence of bounded trajectories via upper and lower solutions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (3) : 575-590. doi: 10.3934/dcds.2000.6.575 |
[11] |
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 |
[12] |
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 & Continuous Dynamical Systems - B, 2020, 25 (2) : 617-633. doi: 10.3934/dcdsb.2019257 |
[13] |
Armengol Gasull, Hector Giacomini, Joan Torregrosa. Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3567-3582. doi: 10.3934/dcds.2013.33.3567 |
[14] |
Nakao Hayashi, Chunhua Li, Pavel I. Naumkin. Upper and lower time decay bounds for solutions of dissipative nonlinear Schrödinger equations. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2089-2104. doi: 10.3934/cpaa.2017103 |
[15] |
Gang Li, Fen Gu, Feida Jiang. Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1449-1462. doi: 10.3934/cpaa.2020071 |
[16] |
Ana Maria Bertone, J.V. Goncalves. Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 315-328. doi: 10.3934/dcds.2000.6.315 |
[17] |
Abdelkader Boucherif. Positive Solutions of second order differential equations with integral boundary conditions. Conference Publications, 2007, 2007 (Special) : 155-159. doi: 10.3934/proc.2007.2007.155 |
[18] |
N. V. Krylov. Uniqueness for Lp-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2495-2516. doi: 10.3934/cpaa.2018119 |
[19] |
Anne Mund, Christina Kuttler, Judith Pérez-Velázquez. Existence and uniqueness of solutions to a family of semi-linear parabolic systems using coupled upper-lower solutions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5695-5707. doi: 10.3934/dcdsb.2019102 |
[20] |
S. E. Kuznetsov. An upper bound for positive solutions of the equation \Delta u=u^\alpha. Electronic Research Announcements, 2004, 10: 103-112. |
2018 Impact Factor: 0.925
Tools
Metrics
Other articles
by authors
[Back to Top]