Polynomial operator matrices as semigroup generators: the 2 x 2 case.
Polynomial Riccati equations with algebraic solutions
We consider the equations of the form dy/dx = y²-P(x) where P are polynomials. We characterize the possible algebraic solutions and the class of equations having such solutions. We present formulas for first integrals of rational Riccati equations with an algebraic solution. We also present a relation between the problem of algebraic solutions and the theory of random matrices.
Polynomial solutions of a generalization of the first Painlevé differential equation.
Polynomial solutions to the Hele--Shaw problem.
Polynomial systems: a lower bound for the weakened 16th Hilbert problem.
In this paper we provide the greatest lower bound about the number of (non-infinitesimal) limit cycles surrounding a unique singular point for a planar polynomial differential system of arbitrary degree.
Population dynamical behavior of a single-species nonlinear diffusion system with random perturbation
We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation.
Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population
Population dynamics of Bithynia tentaculata
Population dynamics with symmetric and asymmetric harvesting.
Population models with nonlinear boundary conditions.
Porous medium equation and fast diffusion equation as gradient systems
We show that the Porous Medium Equation and the Fast Diffusion Equation, , with , can be modeled as a gradient system in the Hilbert space , and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions.
Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument.
Positive almost periodic solutions of non-autonomous delay competitive systems with weak allee effect.
Positive and dead-core solutions of two-point singular boundary value problems with -Laplacian.
Positive and maximal positive solutions of singular mixed boundary value problem
The paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.
Positive and monotone solutions of an -point boundary-value problem.
Positive and oscillating solutions of equation
Positive and oscillatory radial solutions of semilinear elliptic equations.
Positive coefficients case and oscillation
We consider the second order self-adjoint differential equation (1) (r(t)y’(t))’ + p(t)y(t) = 0 on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and converges.
Positive decreasing solutions of systems of second order singular differential equations.