Nonlinear Differential Equations |
Contents
PREFACE | 7 |
SOME EXAMPLES TO BEGIN WITH | 15 |
Nonlinear Systems | 24 |
Copyright | |
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a₁ a₁(x a²u arbitrary assertion assume Banach space boundary conditions boundary value problem c₁ c₂ CAR(p Chapter choose classical solution coefficients coercive concept constant continuous function continuous linear convex convex set corresponds d₁ d²F(u denote derivative dF(u Dirichlet problem du(x Dv(x dx² element Example exists finite formal differential operator formula function defined functional F given function grad u(x growth conditions Hilbert space Hölder inequality holds inf F(u integral Lemma Let F Let the function mapping multi-indexes nonlinear normed linear space obtain order 2k ordinary differential equations possible prove reader reflexive reflexive space relation Remark right-hand side second order SECTION sequence so-called Sobolev space subset symbol u₁ u₂ variables variational inequality vector weak solution weakly ΘΩ ди ди дх ду