Displaying 741 – 760 of 11160

Showing per page

A stochastic model of symbiosis

Urszula Skwara (2010)

Annales Polonici Mathematici

We consider a system of stochastic differential equations which models the dynamics of two populations living in symbiosis. We prove the existence, uniqueness and positivity of solutions. We analyse the long-time behaviour of both trajectories and distributions of solutions. We give a biological interpretation of the model.

A stochastic symbiosis model with degenerate diffusion process

Urszula Skwara (2010)

Annales Polonici Mathematici

We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.

A strongly degenerate quasilinear equation : the elliptic case

Fuensanta Andreu, Vicent Caselles, José Mazón (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation u - div 𝐚 ( u , D u ) = v , where v L 1 , 𝐚 ( z , ξ ) = ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ξ , satisfying other additional assumptions. In particular, this class includes the case where f ( z , ξ ) = ϕ ( z ) ψ ( ξ ) , ϕ > 0 , ψ being a convex function with linear growth as ξ . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the...

A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

The operator L 0 : D L 0 H H , L 0 u = 1 r d d r r d d r 1 r d d r r d u d r , D L 0 = { u C 4 ( [ 0 , R ] ) , u ' ( 0 ) = u ' ' ' ' ( 0 ) = 0 , u ( R ) = u ' ( R ) = 0 } , H = L 2 , r ( 0 , R ) is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on L 0 (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types L 0 u = g and u t t + L 0 u = g , respectively.

A study of resolvent set for a class of band operators with matrix elements

Andrey Osipov (2016)

Concrete Operators

For operators generated by a certain class of infinite three-diagonal matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying second order finite-difference equations. This enables us to describe some asymptotic behavior of the corresponding systems of vector orthogonal polynomials on the resolvent set. We also find that the operators generated by infinite Jacobi matrices have the largest resolvent set in this class.

A study of second order differential inclusions with four-point integral boundary conditions

Bashir Ahmad, Sotiris K. Ntouyas (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.

Currently displaying 741 – 760 of 11160