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Displaying 881 –
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We first introduce the notion of microdifferential operators of WKB type and then develop
their exact WKB analysis using microlocal analysis; a recursive way of constructing a WKB
solution for such an operator is given through the symbol calculus of microdifferential
operators, and their local structure near their turning points is discussed by a
Weierstrass-type division theorem for such operators. A detailed study of the Berk-Book
equation is given in Appendix.
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.
We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.
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