Band 42, Heft 2

In this paper, we introduce a new class of λ-analogues of the Changhee–Hermite polynomials and generalized Gould–Hopper–Appell type λ-Changhee polynomials, and present some properties and identities of these polynomials. A new class of polynomials generalizing different classes of Hermite polynomials such as the real Gould–Hopper, as well as the 1D and 2D holomorphic, ternary and polyanalytic complex Hermite polynomials and their relationship to the Appell type λ-Changhee polynomials are also discussed.

This paper is devoted to the study of the growth of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = 0 , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=0, ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = F , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F, where A i ⁢ j {A_{ij}} ( i = 0 , … , n {i=0,\ldots,n} , j = 0 , … , m {j=0,\ldots,m} ), F are meromorphic functions and c i {c_{i}} ( 0 , … , n {0,\ldots,n} ) are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng.

The prime intention of this paper is to study the conditions under which certain non-linear generalized delay-differential equations possess a solution. In this respect, by extending and improving recent results of [5, 15], we characterize the nature of solutions. By providing relevant examples in a remark, we also show that for the uniqueness of solutions the conditions on the Borel exceptional value can not be removed. Finally, to determine explicitly all forms of the solutions of a traditional generalized delay-differential equation, we deal with the situation under the aegis of generalized c -delay-differential equations. We exhibit some examples to show that the conclusions of the theorems actually occur.

In this article we present sufficient conditions that ensures that normalized Wright functions belong to certain subclasses of analytic univalent functions with negative coefficients in the unit disc 𝒰 {\mathcal{U}} . We also provide some geometric properties of integral transforms involving normalized Wright functions.

The main purpose of this paper is to show the existence of weak solutions for a problem involving the fractional p ⁢ ( x , ⋅ ) {p(x,\cdot\,)} -Laplacian operator of the following form: { ( - Δ p ⁢ ( x , ⋅ ) ) s ⁢ u ⁢ ( x ) + w ⁢ ( x ) ⁢ | u | p ¯ ⁢ ( x ) - 2 ⁢ u = λ ⁢ f ⁢ ( x , u ) in  ⁢ Ω , u = 0 in  ⁢ ℝ N ∖ Ω , \left\{\begin{aligned} \displaystyle(-\Delta_{p(x,\cdot\,)})^{s}u(x)+w(x)% \lvert u\rvert^{\bar{p}(x)-2}u&\displaystyle=\lambda f(x,u)&&\displaystyle% \phantom{}\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{in }\mathbb{R}^{% N}\setminus\Omega,\end{aligned}\right. The main tool used for this purpose is the Berkovits topological degree.