Nonlinear Monotone Potential Operators: From Nonlinear ODE and PDE to Computational Material Sciences
نویسنده
چکیده
This paper deals with boundary value problems for nonlinear monotone potential operators. An analysis of the nonlinear (monotone potential) Sturm–Liouville operator Au := − ( k((u′)2)u′(x) )′+q(x)u(x), x ∈ (a, b) shows that the potential of this operator as well as the potential of related boundary value problems play an important role not only for solvability of these problems, but also for linearization and convergence of solutions of corresponding linearized problems. This approach is then applied to boundary value problems for nonlinear elliptic equations with nonlinear monotone potential operators. As an extension of obtained results in the second part of the paper some applications to computational material science (COMMAT) are proposed. In this context, boundary value problems related to elastoplastic torsion of a bar, and the bending problem for an incompressible plate are considered. AMS Subject Classifications: 47H05, 47H50, 35J65, 35K60, 35A15, 74B20.
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