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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 , SIAM J. Math. Anal., 27 (1996), 515-527.
doi: 10.1137/S0036141093260847. |
[2] |
A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems , J. Math. Anal. Appl., 185 (1994), 302-320.
doi: 10.1006/jmaa.1994.1250. |
[3] |
A. Cabada and R. Enguica, Positive solutions of fourth order problems with clamped beam boundary conditions , Nonlinear Analysis, 74 (2011), 3112-3122.
doi: 10.1016/j.na.2011.01.027. |
[4] |
W. A. Coppel, Disconjugacy. Lecture Notes in Mathematics, 220, Springer-Verlag, Berlin-New York, 1971. |
[5] |
U. Elias, Eigenvalue problems for the equations $Ly + \lambda p(x)y=0$ , Journal of Differential Equations, 29 (1978), 28-57.
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, Dordrecht, The Netherlands, 1997.
doi: 10.1007/978-94-017-2517-0. |
[7] |
M. Gregus, Third order linear differential equations (Mathematics and its Applications), Reidel, Dordrecht, 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 , J. Differential Equations, 13 (1973), 432-437.
doi: 10.1016/0022-0396(73)90002-8. |
[9] |
G. Klaasen, Differential inequalities and existence theorems for second and third order boundary value problems , J. Differential Equations, 10 (1971), 529-537.
doi: 10.1016/0022-0396(71)90010-6. |
[10] |
S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem , J. Math. Anal. Appl., 323 (2006), 413-425.
doi: 10.1016/j.jmaa.2005.10.037. |
[11] |
R. Ma, Multiplicity results for a third order boundary value problem at resonance , Nonlinear Anal., 32 (1998), 493-500.
doi: 10.1016/S0362-546X(97)00494-X. |
[12] |
D. J. O'Regan, Topological transversality: Application to third-order boundary value problem , SIAM J. Math. Anal., 19 (1987), 630-641.
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 , J. Differential Equations, 188 (2003), 461-472.
doi: 10.1016/S0022-0396(02)00146-8. |
[14] |
W. C. Troy, Solution of third order differential equations relevant to draining and coating flows , SIAM J. Math. Anal., 24 (1993), 155-171.
doi: 10.1137/0524010. |
[15] |
Q. Yao and Y. Feng, The existence of solutions for a third order two-point boundary value problem , Appl. Math. Lett., 15 (2002), 227-232.
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 , SIAM J. Math. Anal., 27 (1996), 515-527.
doi: 10.1137/S0036141093260847. |
[2] |
A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems , J. Math. Anal. Appl., 185 (1994), 302-320.
doi: 10.1006/jmaa.1994.1250. |
[3] |
A. Cabada and R. Enguica, Positive solutions of fourth order problems with clamped beam boundary conditions , Nonlinear Analysis, 74 (2011), 3112-3122.
doi: 10.1016/j.na.2011.01.027. |
[4] |
W. A. Coppel, Disconjugacy. Lecture Notes in Mathematics, 220, Springer-Verlag, Berlin-New York, 1971. |
[5] |
U. Elias, Eigenvalue problems for the equations $Ly + \lambda p(x)y=0$ , Journal of Differential Equations, 29 (1978), 28-57.
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, Dordrecht, The Netherlands, 1997.
doi: 10.1007/978-94-017-2517-0. |
[7] |
M. Gregus, Third order linear differential equations (Mathematics and its Applications), Reidel, Dordrecht, 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 , J. Differential Equations, 13 (1973), 432-437.
doi: 10.1016/0022-0396(73)90002-8. |
[9] |
G. Klaasen, Differential inequalities and existence theorems for second and third order boundary value problems , J. Differential Equations, 10 (1971), 529-537.
doi: 10.1016/0022-0396(71)90010-6. |
[10] |
S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem , J. Math. Anal. Appl., 323 (2006), 413-425.
doi: 10.1016/j.jmaa.2005.10.037. |
[11] |
R. Ma, Multiplicity results for a third order boundary value problem at resonance , Nonlinear Anal., 32 (1998), 493-500.
doi: 10.1016/S0362-546X(97)00494-X. |
[12] |
D. J. O'Regan, Topological transversality: Application to third-order boundary value problem , SIAM J. Math. Anal., 19 (1987), 630-641.
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 , J. Differential Equations, 188 (2003), 461-472.
doi: 10.1016/S0022-0396(02)00146-8. |
[14] |
W. C. Troy, Solution of third order differential equations relevant to draining and coating flows , SIAM J. Math. Anal., 24 (1993), 155-171.
doi: 10.1137/0524010. |
[15] |
Q. Yao and Y. Feng, The existence of solutions for a third order two-point boundary value problem , Appl. Math. Lett., 15 (2002), 227-232.
doi: 10.1016/S0893-9659(01)00122-7. |
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