A new criterion for the existence of multiple solutions in cones

作者：Franco Daniel^*; Infante Gennaro; Peran Juan

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2012, 142(5): 1043-1050.

DOI：10.1017/S0308210511001016

We provide new sufficient conditions for the existence of multiple fixed points for a map between ordered Banach spaces. An interesting feature of this approach is that we require conditions not on two boundaries, but rather on one boundary and a point with some extra information on the monotonicity of the nonlinearity on a certain set. We apply our results to prove the existence of at least two positive solutions for a nonlinear boundary-value problem that models a thermostat.

• 出版日期2012-10