Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value |
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Authors: | Yuan Di Wang |
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Institution: | (1) Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China |
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Abstract: | Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for
nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results
for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear
boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces
and generalized Poincaré operators play an important role in proving the existence of solutions.
Supportedpartly by Research Grant 19531060 of China NSF and Grant 97024811 of the Foundation of Doctoral
Program |
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Keywords: | Nonlocal problem Nonlinear boundary condition Parabolic equation Solution Existence Generalized Poincare e operator |
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