Displaying 441 – 460 of 478

Showing per page

Two notions which affected nonlinear analysis (Bernard Bolzano lecture)

Pavel Drábek (2014)

Mathematica Bohemica

General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the p -Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a complete survey....

Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in n . Also, for symmetric second-order ordinary differential operators we show that lim sup t c ( p q ' ) ' / q 2 = θ < 2 where c is a singular point guarantees separation of - ( p y ' ) ' + q y on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that - Δ y + q y is separated on its minimal domain if q is superharmonic. For n = 1 the criterion...

Currently displaying 441 – 460 of 478