Nonlinear Differential Equations

Description

Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations. Content: Studies in Applied MechanicsPage 2 Front MatterPage 3 Copyright pagePage 4 PrefacePages 7-10S. FUČÍK, A. KUFNER List of SymbolsPages 11-14 Chapter I - Some Examples to Begin withPages 15-32 Chapter II - IntroductionPages 33-72 Chapter III - The Weak Solution of a Boundary Value ProblemPages 73-168 Chapter IV - The Variational MethodPages 169-238 Chapter V - The Topological MethodPages 239-273 Chapter VI - Noncoercive ProblemsPages 274-311 Chapter VII - Variational InequalitiesPages 312-352 ReferencesPages 353-356 IndexPages 357-359