‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

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...

Let us quickly recall the main ideas of intersection type lambda calculus (for a recent paper on this topic see [6]). It is well known that the pure lambda calculus Λ (see [2]) formalizes the notion of computable function without any reference to the concepts of domain and co-domain, contrary to what happens in the set theoretic or the categorical approach. The main advantage of this approach i...

We consider a generalization of the gamma function which we term as lambda analogue or $\lambda$-gamma and further, establish some its accompanying properties. For particular case when $\lambda=1$, results established reduce to involving classical function. The techniques employed in proving our are analytical nature.

Before the 1939-1945 war and for some years afterwards Dr Carmichael ran a very successful small discussion group called the Neurological Club. Members were widely recruited and there was a contingent from Cambridge which included Rushton, Hodgkin and Huxley. Rushton was my director of studies as an undergraduate at Cambridge, and I suspect it was because he knew Carmichael through the Neurolog...

B R Calder, L M Linnett and D R Carmichael Heriot-Watt University, Scotland and DRA Bincleaves, England

‎in this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-laplacian oprator and singular nonlinearities‎. ‎we‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ we find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎we use the method ...