Vol. 39, No. 2, 1971

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Nonlinear equations of evolution

Bruce Donald Calvert

Vol. 39 (1971), No. 2, 293–350

We begin by considering various kinds of nonlinear operators in a Banach lattice X, i.e., a Banach space which has a compatible lattice structure. With adequate definitions we are able to develop a theory parallel to the theory of nonlinear equations of evolutions in a general Banach space, as carried out by Komura, Kato, Browder and others. Existence and uniqueness theorems about solutions of the equation of evolution du(t)∕dt = Au(t) are developed under conditions on the space X and the operator A. Given a solution u(t) to du(i)∕dt = Au(t) with initial condition u(0) = v, where v lies in the domain of A, a semi-group U(t) is defined by U(t)v = u(t),t 0.

Mathematical Subject Classification
Primary: 47H15
Received: 11 February 1970
Published: 1 November 1971
Bruce Donald Calvert