Half-Linear Differential Equations
The book presents a systematic and compact treatment of the qualitative theory of half-linear
differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.
- The first complete treatment of the qualitative theory of half-linear differential equations.
- Comparison of linear and half-linear theory.
- Systematic approach to half-linear oscillation and asymptotic theory.
- Comprehensive bibliography and index.
- Useful as a reference book in the topic.
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Assume assumptions asymptotic boundary conditions boundary value problem bounded coefficients comparison theorem consider continuous function contradiction convergent Corollary cosp coupled point criterion defined definition denote disconjugacy disconjugate discrete DOSLY eigenfunction eigenvalue equivalent Euler finite following statement function f given half-linear differential equations half-linear equations Hence Hölder inequality holds implies inequality initial condition initial value problem integral Kusano Lemma Let c(t lim sup liminf linear equation linearly independent Mean Value Theorem nondecreasing nonnegative nonoscillation nonoscillatory solution nontrivial solution Note obtain oscillation criteria oscillation theory p-Laplacian paper periodic function Picone identity previous theorem principal solution proof of Theorem proved Prüfer transformation resp Riccati equation 1.1.21 Riccati technique satisfies second order sequence singular solutions solution of 1.1.1 solvability Sturmian Subsection sufficiently Suppose unique Wronskian zero in a,b