arXiv subjects

Marta García-Huidobro

Publications and source records attributed to Marta García-Huidobro.

3 recordsLinked to original sources

arXiv2026

Monotonicity of the period and positive periodic solutions of a quasilinear equation

We investigate the monotonicity of the minimal period of periodic solutions of quasilinear differential equations involving the $p$-Laplace operator. First, the monotonicity of the period is obtained as a function of a Hamiltonian energy in two cases. We extend to $p\ge2$ classical results due to Chow-Wang and Chicone for $p=2$. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize monotonicity results by Miyamoto-Yagasaki and Benguria-Depassier-Loss to $p\ge2$.

math.AP↗

arXiv2022

Multiplicity results for ground state solutions of a semilinear equation via abrupt changes in magnitude of the nonlinearity

Given $k\in\mathbb N$, we define a class of continuous piecewise functions $f$ having abrupt but controlled magnitude changes so that the problem $$Δu +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetric ground state solutions.

math.AP↗

arXiv2015

Multiplicity results for sign changing bound state solutions of a semilinear equation

In this paper we give conditions on $f$ so that problem $$ Δu +f(u)=0,\quad x\in \mathbb{R}^N, N\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\infty)$. This property will allow us to give conditions on $f$ so that this problem has at least any given number of radial solutions having a prescribed number of zeros.

math.AP↗