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Solvability of a third-order two-point boundary value problem. (English) Zbl 1094.34506
Consider the third-order two-point boundary value problem $$u'''(t)+f(t,u(t))=0,\quad 0\le t\le 1,\quad u(0)=u'(0)=u'(1)=0.\tag*$$ By means of a new maximum principle and the lower and upper solution technique, the authors prove the existence of at least one solution to problem (*).

##### MSC:
 34B15 Nonlinear boundary value problems for ODE
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##### References:
 [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 problem. SIAM J. Math. anal. 19, 630-641 (1987) [4] Troy, W. C.: Solution 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.; Peleter, L. A.: Two problems from draining flows involving third-order ordinary differential equation. 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] Yao, Q.; Feng, Y.: The existence of solutions for a third order two-point boundary value problem. Appl. math. Lett. 15, 227-232 (2002) · Zbl 1008.34010 [9] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM rev. 18, 620-709 (1976) · Zbl 0345.47044