Báo Cáo Báo cáo hóa học NONSMOOTH AND NONLOCAL DIFFERENTIAL EQUATIONS IN LATTICE-ORDERED BANACH SPACES SIEGF

NONSMOOTH AND NONLOCAL DIFFERENTIAL EQUATIONS IN LATTICE-ORDERED BANACH SPACES ¨ SIEGFRIED CARL AND S. HEIKKILA Received 7 September 2004 We derive existence results for initial and boundary value problems in lattice-ordered Banach spaces. The considered problems can be singular, functional, discontinuous, and nonlocal. Concrete examples are also solved. 1. Introduction In this paper, we apply fixed point results for mappings in partially ordered function spaces to derive existence results for initial and boundary value problems in an ordered Banach space E. Throughout this paper, we assume that E satisfies one of the following hypotheses. (A) E is a Banach lattice whose every norm-bounded and increasing sequence is strongly convergent. (B) E is a reflexive lattice-ordered Banach space whose lattice operation E x → x+ = sup{0,x} is continuous and x+ ≤ x for all x ∈ E. We note that condition (A) is equivalent with E being a weakly complete Banach lattice, see, for example