We study several properties of a homotopy solution path associated with continuous nonlinear quasi-monotone complementarity problems. We use Poincare-Bohn’s homotopy invariance theorem of degree to derive an alternative theorem. Based on this result, a sufficient condition is established to assure the existence and boundedness of this homotopy solution path. Our results provide a theoretical ba...

In this article, a two prey - one predator model has been studied where species are competitive in nature and also uses toxic substances for own existence. Biologically well posedness of the system shown through positivity boundedness solutions. Existence criterion stability analysis non-negative equilibrium points have discussed. The sufficient conditions existence Hopf bifurcation switches in...

Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics population cells interacting with chemoattractant nutrient. The former induces chemotactic bias in diffusive motion is accounted by density-suppressed motility. first established generic positive non-increasing motility functions vanishing at...

In this paper, a stochastic Hantavirus infection model is constructed. The existence, uniqueness, and boundedness of the positive solution are derived. conditions for extinction from system obtained. Furthermore, criteria presence unique ergodic stationary distribution established using suitable Lyapunov function. Finally, importance environmental noise in illustrated Milstein method.

In this article, we study a diffusive predator-prey system with prey-taxis under homogeneous Neumann boundary conditions. We establish the existence and boundedness of nonnegative global solutions. Through comparison without prey-taxis, find that positive constant equilibrium remains stable for while negative makes it unstable.

This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and b...

This paper is devoted to the mathematical analysis of a thermomechanical model describing phase transitions in terms of the entropy and order structure balance law. We consider a macroscopic description of the phenomenon and make a presentation of the model. Then, the initial and boundary value problem is addressed for the related PDE system, which contains some nonlinear and singular terms wit...

This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap under conditions that relax the boundedness assumption made by Pennanen and Perkkiö in [Stochastic programs without duality gaps, Math. Program., 136(1):91–1...

The aim of this work is to propose and analyze a new mathematical model formulated by fractional differential equations (FDEs) that describes the dynamics oncolytic M1 virotherapy. well-posedness proposed proved through existence, uniqueness, nonnegativity, boundedness solutions. Furthermore, we study all equilibrium points conditions needed for their existence. We also global stability these i...