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The existence of solution for a third-order two-point boundary value problem. (English) Zbl 1008.34010
Summary: The authors use the lower and upper solutions method and the fixed-point theorem on cones to establish several existence results on a third-order two-point boundary value problem.

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[1] Klaasen, G.: Differential inequalities and existence theorems for second and third order boundary value problems. J. differential equations 10, 529-537 (1971) · Zbl 0211.40001
[2] Jackson, L. K.: Existence and uniqueness of solutions of boundary value problems for third order differential equations. J. differential equations 13, 432-437 (1973) · Zbl 0256.34018
[3] O’regan, D. J.: Topological transversality: application to third order boundary value problems. SIAM J. Math. anal. 19, 630-641 (1987)
[4] Troy, W. C.: Solutions of third-order differential equations relevant to draining and coating flows. SIAM J. Math. anal. 24, 155-171 (1993) · Zbl 0807.34030
[5] Cabada, A.: The method of lower and upper solutions for second, third, fourth and higher order boundary value problems. J. math. Anal. appl. 185, 302-320 (1994) · Zbl 0807.34023
[6] Bernis, F.; Peletier, L. A.: Two problems from draining flows involving third-order ordinary differential equations. SIAM J. Math. anal. 27, 515-527 (1996) · Zbl 0845.34033
[7] Ruyun, M.: Multiplicity results for a third order boundary value problem at resonance. Nonlinear anal. 32, 493-500 (1998) · Zbl 0932.34014
[8] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM rev. 18, 620-709 (1976) · Zbl 0345.47044