The paper is devoted to integro-differential operators, which correspond to nonlocal reaction-diffusion equations considered on the whole axis. Their Fredholm property and properness will be proved.… (More)

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method. 1.… (More)

Infinite-dimensional difference operators are studied. Under the assumption that the coefficients of the operator have limits at infinity, limiting operators and associated polynomials are… (More)

M. Alfaro, N. Apreutesei, F. Davidson, V. Volpert 1 I3M, University Montpellier 2, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France 2 Department of Mathematics, “Gheorghe Asachi”… (More)

An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds… (More)

where A : D(A)⊆H →H , α : D(α)⊆H →H , and β : D(β)⊆H →H are maximal monotone operators in the real Hilbert space H (satisfying some specific properties), a, b are given elements in the domain D(A) of… (More)