Volume 29, Issue 5

Effective sufficient conditions are established for the well-posedness of the Cauchy problem with weight for linear systems of generalized ordinary differential equations with singularities. The results are realized for impulsive differential systems.

In this paper, the notion of generalized derivations is characterized. Also, the action of these derivations on ideals is investigated and as a consequence, some results involving commutator identities are proved. Further, we explore the commutativity of prime additively inverse semirings in which generalized derivations satisfy certain differential identities. An extension to Posner’s second theorem is also established in the framework of generalized derivations.

Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff model coupled with the unsteady heat system govern the fluid motion. This contribution is an extension of the previous established works. The novelty of this paper is to supply a close scrutiny result of the spawned interface through the medium of the pervasive Schauder fixed point. Numerical results are exhibited to illustrate the effectiveness of the advocated approach.

In this paper, we investigate the ground states for the following fractional Choquard equation with magnetic fields and critical exponents: ( - Δ ) A s ⁢ u + V ⁢ ( x ) ⁢ u = λ ⁢ f ⁢ ( x , u ) + [ | x | - α ∗ | u | 2 α , s * ] ⁢ | u | 2 α , s * - 2 ⁢ u   in  ⁢ ℝ N , (-\Delta)_{A}^{s}u+V(x)u=\lambda f(x,u)+[\lvert x\rvert^{-\alpha}\ast\lvert u% \rvert^{2^{*}_{\alpha,s}}]\lvert u\rvert^{2^{*}_{\alpha,s}-2}u\quad\text{in }% \mathbb{R}^{N}, where λ > 0 {\lambda>0} , α ∈ ( 0 , 2 ⁢ s ) {\alpha\in(0,2s)} , N > 2 ⁢ s {N>2s} , u : ℝ N → ℂ {u:\mathbb{R}^{N}\rightarrow\mathbb{C}} is a complex-valued function, 2 α , s * = ( 2 ⁢ N - α ) / ( N - 2 ⁢ s ) {2^{*}_{\alpha,s}=(2N-\alpha)/(N-2s)} is the fractional Hardy–Littlewood–Sobolev critical exponent, V ∈ ( ℝ N , ℝ ) {V\in(\mathbb{R}^{N},\mathbb{R})} is an electric potential, V and f are asymptotically periodic in x , A ∈ ( ℝ N , ℝ N ) {A\in(\mathbb{R}^{N},\mathbb{R}^{N})} is a magnetic potential, and ( - Δ ) A s {(-\Delta)^{s}_{A}} is a fractional magnetic Laplacian operator with s ∈ ( 0 , 1 ) {s\in(0,1)} . We prove that the equation has a ground state solution for large λ by using the Nehari method and the concentration-compactness principle.

In this paper, by using invariants of Riemann and general solutions of Euler–Poisson–Darboux–Riemann equations, a new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics is given.

Fubini polynomials play an important role in the theory and applications of mathematics. These polynomials appear in combinatorial mathematics, thus attracted an appreciable amount of interest of number theory and combinatorics experts. In this paper, the q -Fubini polynomials are combined with q -Bessel functions in order to introduce q -Fubini–Bessel functions. Certain results for these q -hybrid functions are derived. Their relations with the classical Fubini polynomials and Bessel functions are established and q -Fubini–Bessel polynomials are explored. The graphical representations of q -Fubini polynomials and q -Fubini–Bessel polynomials for particular values of indices and variables are also considered.

The aim of this paper is to represent any polynomial in terms of degenerate Frobenius–Euler polynomials and, more generally, of higher-order degenerate Frobenius–Euler polynomials. Explicit formulas with the help of umbral calculus are derived and the obtained results are illustrated by some examples.

In the present paper, the sufficient conditions are obtained for the generalized β-absolute convergence ( 0 < β < 2 ) {(0<\beta<2)} of the Fourier trigonometric series with gaps for some classes of functions. In [8], analogous problems were considered for Fourier trigonometric series and sufficient conditions were established in terms of the δ-variation of a function; also, it was proved that these conditions are unimprovable in a certain sense. Our goal is to show that if a function f has a Fourier series with gaps, then the results obtained in [8] hold if the function f satisfies the derived conditions only on an arbitrarily small interval.

In this paper, the inverse of Berge’s maximum theorem is established in a locally convex topological vector space. Using this result, the generalized Gale–Nikaido–Debreu’s lemma and the generalized coincidence point theorem are derived from the equilibrium theorem of generalized games. By combining the inverse of Berge’s maximum theorem with the generalized coincidence point theorem, the equilibrium theorem of the generalized game is obtained immediately. Finally, we show that Fan–Glicksberg’s fixed point theorem and von Neumann’s lemma can be derived directly from the coincidence point theorem.

Some statements connected with the ( C , - 1 < α < 0 , - 1 < β < 0 ) {(C,-1<\alpha<0,-1<\beta<0)} summability almost everywhere of double series with respect to block-orthonormal systems are given. In particular, using the obtained results, we can determine Weyl multipliers for establishing negative order summability of double series with respect to Δ p , q {\Delta_{p,q}} -ONS.

The purpose of this paper is to prove the finiteness theorems for meromorphic mappings of a complete connected Kähler manifold into a projective space sharing few hyperplanes in subgeneral position without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. Our results are extensions and generalizations of some recent ones.