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- W2057223639 abstract "For a given closed and translation invariant subspace<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Y$ id=E1><mml:mi>Y</mml:mi></mml:math>of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$uin Y$ id=E2><mml:mrow><mml:mi>u</mml:mi><mml:mo>∈</mml:mo><mml:mi>Y</mml:mi></mml:mrow></mml:math>to the equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$u^{prime}(t)+ A(u(t))+omega u(t)ni f(t),tinmathbb{R}$ id=E3><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>ω</mml:mi><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∍</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi></mml:mrow></mml:math>, or of solutions<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$u$ id=E4><mml:mi>u</mml:mi></mml:math>asymptotically close to<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Y$ id=E5><mml:mi>Y</mml:mi></mml:math>for the inhomogeneous differential equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$u^{prime}(t)+ A(u(t))+omega u(t)ni f(t),t > 0, u(0)= u_0$ id=E6><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>ω</mml:mi><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∍</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>></mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, in general Banach spaces, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A$ id=E7><mml:mi>A</mml:mi></mml:math>denotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Y$ id=E8><mml:mi>Y</mml:mi></mml:math>are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior." @default.
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- W2057223639 title "Bounded solutions of nonlinear Cauchy problems" @default.
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