The existence of a positive solution for the generalized predator-prey model for two species $$ \begin{gathered} \Delta u + u(a + g(u,v)) = 0\quad \mbox {in}\ \Omega ,\\ \Delta v + v(d + h(u,v)) = 0\quad \mbox {in} \ \Omega ,\\ u = v = 0\quad \mbox {on}\ \partial \Omega , \end{gathered} $$ are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.
Dually residuated lattice ordered monoids (DRl-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (MV -algebras, BL-algebras) and their non-commutative variants (GMV - algebras, pseudo BL-algebras). In the paper, lex-extensions and lex-ideals of DRl-monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.
A mathematical model of the roadway automobile motion is numerically analyzed. This model is intended to describe the roadway automobile stability. A previous paper [6] described the model in detail and the general method of qualitative analysis. In the present paper, we continue the discussion of stability by numerical simulations and the specific question we attempted to answer is: which parameter(s) of automobile geometry and quality of the roadway can serve as a reliable predictors) for car crash? Data from Daimler-Chrysler AG and Ford Motor Company Limited were used for that purpose, considering three car types - Mercedes-Benz E 320 (T-modelle), Ford Focus and Mercedes-Benz Sprinter (1). Hence, one can consider the present work as a natural continuation of [6]., Obsahuje seznam literatury, and Článek doplňuje Appendix na str. 294-295