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Positive solutions for a class of nonresonant m-point boundary value problems

Feng M., Zhang X., Ge W.

Journal of Applied Analysis

2008

Vol. 14, nr 1

115-129

This paper concerns the existence and multiplicite of positive solutions for a class of nonresonant m-point boundary-value problem of second-order diferential equations Lx = λw(t)(t, x), 0ρ -integrable for some 1≤ p ≤ +∞. the arguments are based upen fixed point theorems in a cone and Hoelder's inequqlity. The nonexistence of positive solution is also studied. In addistion, some examples are included to demonstrate the main results.

Positive solutions to polynomial matrix equations

Kaczorek T.

Applied Mathematics and Computer Science

1998

Vol. 8, no 2

403-415

Necessary and sufficient conditions are established for the existence of positive solutions to polynomial matrix equations. Two methods are proposed for determination of such solutions. As an example of applications it is shown that the determination of the transfer matrix of a positive controller for a closed-loop system with a given transfer matrix can be reduced to finding solutions to two suitable polynomial matrix equations.