Existence theorems for a semilinear elliptic boundary value problem
Salvatore A. Marano (1994)
Annales Polonici Mathematici
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Salvatore A. Marano (1994)
Annales Polonici Mathematici
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Vy Le, Klaus Schmitt (1996)
Banach Center Publications
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We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
Donchev, Tzanko, Ivanov, Radostin (2001)
Novi Sad Journal of Mathematics
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Tsalyuk, Vadim Z. (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Giuseppe Conti, Valeri Obukhovskiĭ, Pietro Zecca (1996)
Banach Center Publications
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In this paper we show that the set of all mild solutions of the Cauchy problem for a functional-differential inclusion in a separable Banach space E of the form x’(t) ∈ A(t)x(t) + F(t,xt) is an -set. Here A(t) is a family of linear operators and F is a Carathéodory type multifunction. We use the existence result proved by V. V. Obukhovskiĭ [22] and extend theorems on the structure of solutions sets obtained by N. S. Papageorgiou [23] and Ya. I. Umanskiĭ [32].
Azzeddine Bellour (2011)
Matematički Vesnik
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Sababheh, M., Khalil, R. (2009)
The Journal of Nonlinear Sciences and its Applications
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Lajkó, Károly, Mészáros, Fruzsina (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Sven Bartels, Diethard Pallaschke (1994)
Applicationes Mathematicae
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Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel...
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.
Haluška, Ján, Hutník, Ondrej (2010)
Banach Journal of Mathematical Analysis [electronic only]
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Krzysztof Czarnowski (1994)
Annales Polonici Mathematici
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The set of solutions of a Volterra equation in a Banach space with a Carathéodory kernel is proved to be an , in particular compact and connected. The kernel is not assumed to be uniformly continuous with respect to the unknown function and the characterization is given in terms of a B₀-space of continuous functions on a noncompact domain.