In this paper, we study the (newly introduced) class of functions called semi-c-periodic functions of type I with values in a Banach space. We first investigate their basic properties, including a convolution result and invertibility of abstract convolution operators on suvh function space. We prove that an important subclass of such functions is a Banach space under the sup-norm. We then study the existence and uniqueness of semi-cperiodic mild solutions for both autonomous and non-autonomous linear evolution equations. We achieve the existence results using the Banach fixed point theorem and the method of reduction.
The rings considered in this paper are commutative with identity and are nonzero. An ideal of a ring is said to be nonnil if it contains an element that is not nilpotent. Let R be a ring. We say that R is nonnil-Noetherian (resp., nonnil-Laskerian) if each proper nonnil ideal of R is finitely generated (resp., each proper nonnil ideal of R admits a primary decomposition). Whenever R is a subring of a ring T, then it is assumed that R contains the identity element of T. Let R subset of T be rings. We say that (R, T) is a nonnil-Noetherian pair (resp., nonnil-Laskerian pair) if each intermediate ring A between R and T is nonnil-Noetherian (resp., nonnil-Laskerian). This paper aims to characterize R such that (R, R[X]) is a nonnil-Noetherian pair (resp., nonnil-Laskerian pair), where R[X] is the polynomial ring in one variable X over R. Also, this paper aims to characterize pairs of the form (R, R[X]) such that each intermediate ring A between R and R[X] has a property that is related to being nonnil-Noetherian (resp., nonnil-Laskerian).
This paper is concerned with the positive solutions of a Matukumatype nonlinear equation with double singular terms, triangle(p)u+ |x|(m1) u(delta 1) + |x|(m2) u(delta 2) = 0, x is an element of R-N, where p > 2, N >= 1, delta(2) > delta(1)>= 1, -p
Let S = K[x(1), ... ,x(n)] be the ring of polynomials over a field K and let I be a monomial ideal of S. We prove that the following are equivalent: (i) I is principal, (ii) hdepth(I) = n, (iii) hdepth(S/I) = n-1. If I is squarefree, we prove that if hdepth(S/I) < 3 or n <= 5, then hdepth(I) >= hdepth(S/I) + 1. Also, we prove that if hdepth(S/I) <5 or n <= 7, then hdepth(I) >= hdepth(S/I).
In this study, we explore the existence of multiple solutions for a dynamic Sturm-Liouville boundary value problem on time scales that incorporate impulsive effects. Utilizing variational methods and applying certain critical point theorems from Ricceri for smooth functionals, we demonstrate the existence of at least three solutions to the problem. To illustrate the practical relevance of our findings, we provide an example at the end.
