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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...

Positive almost automorphic solutions for some nonlinear delay integral equations.

Long, Wei, Ding, Hui-Sheng (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for a system of fractional boundary value problems

Henderson, Johnny, Luca, Rodica (2017)

Proceedings of Equadiff 14

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.

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation $x (t) = \int_{- \infty}^{\infty} h (t - s) f (s, x (s)) d s$ .

Positive solutions of integrodifferential equations.

Philos, Ch.G. (1993)

Journal of Applied Mathematics and Stochastic Analysis

Positive solutions of nonlinear delay integral equations modelling epidemics and population growth.

A. Cañada, A. Zertiti (1993)

Extracta Mathematicae

Positive solutions of quasilinear elliptic systems with strong dependence on the gradient.

Žubrinić, D. (2000)

Acta Mathematica Universitatis Comenianae. New Series

Positive solutions of Volterra integro-differential equations.

Wu, Yumei (1995)

Acta Mathematica Universitatis Comenianae. New Series

Positivity and Regularity of Hyperbolic Volterra Equations in Banach Spaces.

Jan Prüss (1987/1988)

Mathematische Annalen

Predictor-corrector methods for nonlinear Volterra integral equations of the second kind

Günter Porath (1984)

Banach Center Publications

Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint.

Becker, Leigh C. (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Principe d'extremum relatif aux solutions de l'équation intégro-différentielle du processus stochastique markovien mixte

M. Krzyżański (1965)

Annales Polonici Mathematici

Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek, Janusz Morawiec (2009)

Annales Polonici Mathematici

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 $F (x) = \int_{Ω} F (τ (x, ω)) P (d ω)$ in the class of probability distribution functions.

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