Concavity properties for quasilinear equations and optimality remarks

Abstract

In this paper we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schrödinger equations of the type $$-\mathrm{div}(a(u)\nabla u)+\frac{a^{\prime }(u)}{2}|\nabla u{|}^2=f(u)in\; \Omega ,$$ where $\Omega$ is a convex bounded domain of ${\mathbb{R}}^N$. In particular, we search for a function $\phi :\mathbb{R}\to \mathbb{R}$, modeled on $f\in C^1$ and $a\in C^1$, which makes $\phi (u)$ concave. Moreover, we discuss the optimality of the conditions assumed on the source.

To be published on Differential and Integral Equations

Cited by in corpus (1)

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