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Let 𝑋 be a smooth and connected projective curve. Assume the existence of spanned 𝐿 ∈ Pic 𝑎 (𝑋), 𝑅 ∈ Pic 𝑏 (𝑋) such that ℎ 0 (𝑋, 𝐿) = ℎ 0 (𝑋, 𝑅) = 2 and the induced map φ 𝐿,𝑅 : 𝑋 → 𝐏 1 × 𝐏 1 is birational onto its image. Here we study...
A kind of higher order sub-and super-linear FDE with impulses is studied in this paper. Several criteria on the oscillations of solutions are given. In particular, in the case where the coefficients of equations are positive and continuous functions, we find some suitable impulse functions such...
We give upper bounds for the order of the elements in a characteristic set of a regular differential ideal or a radical of a finitely generated differential ideal with respect to some specific orderings. We then show how to compute characteristic sets of these ideals using algebraic methods.
Let 𝑓 be a 2π-periodic function in 𝐿 1 –π, π and be its lacunary Fourier series with small gaps. We have estimated Fourier coefficients of 𝑓 if it is of φ∧ 𝐵𝑉 locally. We have also obtained a precise interconnection between the lacunarity in such series and the localness of...
A functor responsible for second obstruction problems is defined and investigated on the category of topological spaces. In terms of this functor we formulate and prove a classification theorem for maps, which is the reformulation of all known classification theorems for the second obstruction.
We consider the nonlinearly damped semilinear Petrovsky equation and prove the global existence of its solutions by means of the stable set method in combined with the Faedo–Galerkin procedure. Furthermore, we study the asymptotic behavior of solutions when the nonlinear dissipative term 𝑔...
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