On the method of upper and lower solutions in abstract cones
V. Lakshmikantham, S. Leela (1983)
Annales Polonici Mathematici
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V. Lakshmikantham, S. Leela (1983)
Annales Polonici Mathematici
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Tsz Ho Chan (2006)
Acta Arithmetica
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Gavioli, Andrea (1998)
Journal of Convex Analysis
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Brandi, Primo, Salvadori, Anna (1994)
Journal of Convex Analysis
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L. Gajek (1987)
Applicationes Mathematicae
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Plubtieng, Somyot, Sitthithakerngkiet, Kanokwan (2011)
Fixed Point Theory and Applications [electronic only]
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Irena Rachůnková (1997)
Annales Polonici Mathematici
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We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.
Manzini, Giovanni (1998)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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He, Yun-Peng, Xu, Jiu-Ping, Huang, Nan-Jing, Wu, Meng (2010)
Fixed Point Theory and Applications [electronic only]
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Molaei, M.R., Farhangdoost, M.R. (2006)
APPS. Applied Sciences
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Vasil'ev, V.A. (2004)
Journal of Mathematical Sciences (New York)
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Im, Sung Mo, Rim, Dong Il, Kim, Won Kyu (1998)
International Journal of Mathematics and Mathematical Sciences
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Al-Refai, Mohammed, Katatbeh, Qutaibeh (2006)
International Journal of Mathematics and Mathematical Sciences
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Ada Aruffo, Gianfranco Bottaro (2008)
Bollettino dell'Unione Matematica Italiana
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In [7] W.A. Kirk and L.M. Saliga and in [3] Y. Chen, Y.J. Cho and L. Yang introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as some sufficient conditions for the existence of minima, Ekeland's variational principle and Caristi's fixed point theorem, remain still true under lower semicontinuity from above. In the second of the above papers the authors also conjectured that, for convex functions...
J. Kaczorowski, A. Perelli (2012)
Acta Arithmetica
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Plubtieng, Somyot, Sitthithakerngkiet, Kanokwan (2011)
Fixed Point Theory and Applications [electronic only]
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