Linear and nonlinear abstract equations with parameters |
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Authors: | Veli Shakhmurov |
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Affiliation: | Okan University, Department of Electronics and Communication, Akfirat, Tuzla 34959 Istanbul, Turkey |
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Abstract: | This paper focuses on nonlocal boundary value problems for linear and nonlinear abstract elliptic equations in Banach spaces. Here equations and boundary conditions contain certain parameters. The uniform separability of the linear problem and the existence and uniqueness of maximal regular solution of nonlinear problem are obtained in Lp spaces. For linear case the discreteness of spectrum of corresponding parameter dependent differential operator is obtained. The behavior of solution when the parameter approaches zero and its smoothness with respect to the parameter is established. Moreover, we show the estimate for analytic semigroups in terms of interpolation spaces. This fact can be used to obtain maximal regularity properties for abstract boundary value problems. |
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Keywords: | 34G10 35J25 35J70 |
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