Oscillation Theory |
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Contents
Chapter | 1 |
A Generalized SturmPicone Theorem | 11 |
PARTIAL DIFFERENTIAL EQUATIONS | 17 |
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abstract analogous boundary conditions Chapter coefficients comparison theorems conjoined solution conjugate points consider Corollary corresponding defined denote differential equations differential inequalities dx dx eigenfunction elliptic equations elliptic operator establish oscillation exists Green's function Green's theorem Hamiltonian system ij dx integral interval Kreith Lemma maximum principles nodal domain nonnegative definite nonoscillation nonselfadjoint equations nonsingular nontrivial solution u(x obtain ordinary differential oscillation criteria oscillation properties oscillation theory oscillatory behavior P₁ P₁(x P₁j P₂ P₂(x physical interpretation Picone identity Picone identity 1.4 positive operator proof of Theorem Prüfer transformation representation respectively result Riccati equation satisfies scalar selfadjoint selfadjoint equations singularities solution of 7.3 solution of Lv strongly elliptic systems Sturm-Picone theorem Sturmian comparison theorem Swanson symmetric matrix techniques Theorem 1.3 tion u-regular value problems variational vector zeros of u(x ΣΡ ди ди ди дх