We study the fractional difierential equation Dfiu(t) + BDflu(t) + Au(t) = f(t); 0 • t • 2… (0 < fl < fi • 2) in periodic Lebesgue spaces.
Research Interests:
We use operator-valued Fourier multiplier theorems to study second order differential equations in Banach spaces. We establish maximal regularity results in Lp and Cs for strong solutions of a complete second order equation. In the second... more
We use operator-valued Fourier multiplier theorems to study second order differential equations in Banach spaces. We establish maximal regularity results in Lp and Cs for strong solutions of a complete second order equation. In the second part, we study mild solutions for the second order problem. Two types of mild solutions are considered. When the operator A involved is the
Research Interests:
We obtain spectral conditions that characterize mild well-posed inhomogeneous differential equations in a general Banach space X. L p periodic solutions of first and second-order equations are considered. The results are expressed in... more
We obtain spectral conditions that characterize mild well-posed inhomogeneous differential equations in a general Banach space X. L p periodic solutions of first and second-order equations are considered. The results are expressed in terms of operator-valued Fourier multipliers. Our approach provides a unified framework for various notions of strong and mild solutions. Applications to semilinear equations of second order in Hilbert spaces are given.