MMN-21

On periodic-type boundary value problems for functional differential equations with positively homogeneous operator

Abstract

Consider the problem $$ u'(t)=H(u)(t)+Q(u)(t),\qquad u(a)-\lambda u(b)=h(u), $$ where $H,Q:C([a,b];\mathbb{R})\to L([a,b];\mathbb{R})$ are continuous operators satisfying the Carath\`eodory condition, the operator $H$ is positively homogeneous, $\lambda\in \mathbb{R}_+$, and $h:C([a,b];\mathbb{R})\to \mathbb{R}$ is a continuous functional. In this paper, efficient sufficient conditions guaranteeing the solvability and unique solvability of the problem considered are established.


Vol. 5 (2004), No. 1, pp. 33-55
DOI: https://doi.org/10.18514/MMN.2004.21


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