Oscillation Results for Differential Systems
作者： Ravi P. Agarwal , Said R. Grace , Donal O’Regan
DOI: 10.1007/978-94-017-2515-6_7
关键词: Scalar (mathematics) 、 Applied mathematics 、 Differential equation 、 Sublinear function 、 Oscillation theory 、 Linear differential equation 、 Eigenvalues and eigenvectors 、 Nonlinear system 、 Coefficient matrix 、 Mathematics
摘要: In this chapter we are concerned with the oscillation of nonlinear two-dimensional differential systems and second order vector-matrix equations. Section 7.1 shall present criteria for systems. This includes superlinear, linear, sublinear cases. 7.2 deals linear Here, first system considered will be reduced to a certain scalar Riccati inequality, so that known results from literature can applied obtain criteria. Then, employ notation definitions 6.1 some general results. Finally, use variational techniques which involve assumptions on behavior eigenvalues coefficient matrix (or its integral) number sufficient conditions guarantee 7.3 discuss functionally commutative coefficients. show theory such effectively study diagonal 7.4 prove comparison theorems Hille-Wintner type operator-valued 7.5 forcing term given.
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