Nonsmooth and nonlocal differential equations in lattice-ordered Banach spaces (Q934784)

Consider in an ordered Banach space \(E\) the following initial and boundary value problems \[ \begin{aligned} {d\over dt}(p(t) u(t))&= f(t,u)\text{ for a.e. }t\in J:= (a,b),\quad \lim_{t\to a^+} p(t)u(t)= c(u),\tag{1} \\ \text{where \(-\infty\leq a< b\leq+\infty\),} {d\over dt} (p(t) u'(t))&= f(t, u)\text{ for a.e. }t\in J,\quad \lim_{t\to a^+} p(t) u'(t)= c(u),\quad \lim_{t\to a^+} u(t)= d(u),\tag{2}\\ -{d\over dt}(p(t) u'(t))&= f(t,u)\text{ for a.e. }t\in J,\quad \lim_{t\to a^+} p(t) u'(t)= c(u),\quad \lim_{t\to b^-} u(t)= d(u).\tag{3}\end{aligned} \] The authors apply fixed point results for mappings in partially ordered function spaces to derive existence results for (1)--(3). The considered problems include many kinds of special types, such as (a) singular problems, (b) discontinuous nonlinearities, (c) problems of random type.