Svatoslav Staněk (1993)
Annales Polonici Mathematici
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A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
Xingbao Wu (1995)
Annales Polonici Mathematici
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A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.
Hua, Jun, Moseley, James L. (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Jan Kowalski (1994)
Banach Center Publications
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Plotnikov, P.I., Klepacheva, A.V. (2001)
Sibirskij Matematicheskij Zhurnal
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Guedda, L., Hallouz, A. (2008)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Dong, Xin, Bai, Zhanbing (2008)
The Journal of Nonlinear Sciences and its Applications
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Alimohammady, M., Shahmari, A. (2009)
The Journal of Nonlinear Sciences and its Applications
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Klimov, V.S., Pavlenko, A.N. (2001)
Sibirskij Matematicheskij Zhurnal
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Aamri, Mohamed, Bennani, S., El Moutawakil, Driss (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Gerd Herzog (1998)
Colloquium Mathematicae
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We prove that the initial value problem x’(t) = f(t,x(t)), is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.