Point Approximation of a Space-Homogeneous Transport Equation.
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...
We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.
An existence theorem is proved for the scalar convolution type integral equation .
Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation in the class of probability distribution functions.