Jan Bochenek (1991)
Annales Polonici Mathematici
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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.
Jan Bochenek (1995)
Annales Polonici Mathematici
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This paper is devoted to the investigation of the abstract semilinear initial value problem , in the “hyperbolic” case.
L. H. Erbe, W. Krawcewicz, Shaozhu Chen (1991)
Annales Polonici Mathematici
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Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
Xue Zhiqun (2006)
Kragujevac Journal of Mathematics
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Chistyakov, V.V. (2005)
Sibirskij Matematicheskij Zhurnal
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D. O'Regan (1991)
Annales Polonici Mathematici
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Existence of positive solution to certain classes of singular and nonsingular third order nonlinear two point boundary value problems is examined using the idea of Topological Transversality.
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.
Chistyakov, V.V. (2005)
Sibirskij Matematicheskij Zhurnal
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Bogdan Przeradzki (1993)
Colloquium Mathematicae
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Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.
Korobkov, M.V. (2002)
Sibirskij Matematicheskij Zhurnal
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B. Przeradzki (1992)
Annales Polonici Mathematici
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The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.
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.
Ashordia, M. (1996)
Georgian Mathematical Journal
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Thierry De Pauw (2007)
Journées Équations aux dérivées partielles
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