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We provide a generalization of a well known Krasnosel'skii theorem on continuity of the Nemytskii operator for functions taking values in separable Banach spaces. We follow the results obtained in Evans, Partial Differential Equations, Graduate Studies in Mathematics, Amer. Math. Soc., 1998 for...
We consider the problem u tt + δu t + ϵa Δ u + φ ( ∫ Ω |∇ u | 2 dx )Δ u ≥ f ( x , t ), posed in Ω × (0, +∞). Here is a an open smooth bounded domain and φ is like φ ( s ) = bs γ , γ > 0, a > 0 and ϵ = ±1. We prove, in certain conditions on f and φ that there is absence of...
We examine functions of two variables whose all vertical sections are equiderivatives. In particular we show that a bounded function whose horizontal sections are strongly measurable and vertical sections are equiderivatives, is strongly measurable. The theorems we prove are generalizations of...
The conditions of solvability and description of all solutions of the truncated Stieltjes moment problem are obtained using as the starting point earlier results on the Hamburger truncated moment problem. An algebraic algorithm for the explicit solution of both problems is proposed.
In the paper we formulate an axiom , which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to w 1 , while 𝔠 = w 2 : the...
I investigate an asymmetric product construction for ॣ -ideals of ॣ -algebras of sets, corresponding to one-sided Fubini and Kuratowski-Ulam theorems, examining the cellularities of these products.
In this paper, we give two new maximal element theorems in l.c. metric spaces, and as their applications, a new coincidence theorem and two new existence theorems of solutions for generalized quasivariational inequalities are obtained.
In the paper the existence and continuous dependence of a kind of minimax solution to the dual Hamilton-Jacobi equations is proved. The main difficulties which appear here are a special type of the boundary conditions and the transversality conditions which that solution must satisfy. That type...
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