Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations |
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| Authors: | V.Yu. Slyusarchuk |
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| Affiliation: | 1.National University of Water Management and Nature Resources Use,Rivne,Ukraine |
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| Abstract: | Let E be a finite-dimensional Banach space, let C0(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C 0(R ,E) → C 0(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C 0(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation | fracdx(t)dt + ( Kx )(t)Ax(t) = h(t), t ? mathbbR frac{{dx(t)}}{{dt}} + left( {Kx} right)(t)Ax(t) = h(t),quad t in mathbb{R} |
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