Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain

AbstractWe are concerned with proving existence of one or more than one positive solution of a general two point boundary value problem for the nonlinear equation Lx(t)≔−[p(t)xΔ(t)]Δ+q(t)xσ(t)=λa(t)f(t,xσ(t)). We shall also obtain criteria which leads to nonexistence of positive solutions. Here the independent variable t is in a “measure chain”. We will use fixed point theorems for operators on a Banach space

SUBFUNCTIONS FOR THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract not availabl

SUBFUNCTIONS FOR THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract not availabl

Factoring linear differential operators on measure chains

We extend to measure chains Abel's theorem, the existence of a set of positive Wronskians, and the Polya and Trench factorizations of disconjugate linear -differential operators.</p