Quasilinearization Technique for Φ-Laplacian Type Equations

Copyright q 2012 I. Yermachenko and F. Sadyrbaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. An equation d/dt Φ t, x′ f t, x 0 is considered together with the boundary conditions Φ a, x′ a 0, x b 0. This problem under appropriate conditions can be reduced to quasilinear problem for two-dimensional differential system. The conditions for existence ofmultiple solutions to the original problem are obtained by multiply applying the quasilinearization technique.