We introduce, and study, the regularity normality in ideal bitopological spaces, absent subject literature. Our definitions have advantage of using only open sets two underlying topologies. These new concepts represent generalizations Kelly’s pairwise normality. The extension T0, T1 T2 axioms to these spaces is due Caldas et al.

In this short note, we prove that if u solves $$(\partial _t - \Delta )^s = Vu$$ in $${\mathbb {R}}^n_x \times {\mathbb {R}}_t$$ , and vanishes to infinite order at a point $$(x_0, t_0)$$ then $$u \equiv 0$$ . This sharpens (and completes) our earlier result proves $$u(\cdot t) for $$t \le t_0$$ it

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

Abstract Let Q be a differential operator of order $$\le 1$$ ≤ 1 on complex metric vector bundle $$\mathscr {E}\rightarrow \mathscr {M}$$ E → M with connection $$\nabla $$ ∇ over possibly noncompact Rie...