Displaying similar documents to “An improved exponential decay result for some semilinear integrodifferential equations”

Solvability of a generalized third-order left focal problem at resonance in Banach spaces

Youwei Zhang (2013)

Mathematica Bohemica

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This paper deals with the generalized nonlinear third-order left focal problem at resonance ( p ( t ) u ' ' ( t ) ) ' - q ( t ) u ( t ) = f ( t , u ( t ) , u ' ( t ) , u ' ' ( t ) ) , t ] t 0 , T [ , m ( u ( t 0 ) , u ' ' ( t 0 ) ) = 0 , n ( u ( T ) , u ' ( T ) ) = 0 , l ( u ( ξ ) , u ' ( ξ ) , u ' ' ( ξ ) ) = 0 , where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions...

Semilinear evolution equations of the parabolic type

Jan Bochenek (1999)

Annales Polonici Mathematici

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This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.