Abstract
In this paper, we study several quasilinear PDEs with a particular algebraic structure. In the case of stationary solutions for a quasilinear Schrödinger equation, Colin and Jeanjean (Nonlinear Anal 56:213–226, 2004) implemented a dual approach to prove existence and qualitative properties of the solutions. The method takes advantage of the particular underlying structure of that quasilinear PDE, which is essentially semilinear. The main goal of this manuscript is to show that the dual approach is successful in a broader set of problems, especially in the stationary cases involving more general quasilinear terms and the p-Laplacian. We prove also that this approach works for some quasilinear heat equations, but fails for the complete evolution of quasilinear Schrödinger equations. The reason of the failure seems related to the extra structure of the complex plane.
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