arXiv subjects

Joao Marcos do Ó

Publications and source records attributed to Joao Marcos do Ó.

2 recordsLinked to original sources

arXiv2019

The Nehari manifold for indefinite Kirchhoff problem with Caffarelli-Kohn-Nirenberg type critical growth

In this paper we study the following class of nonlocal {problems} involving Caffarelli-Kohn-Nirenberg type critical growth \begin{align*} L(u)&-λh(x)|x|^{-2(1+a)}u=μf(x)|u|^{q-2}u+|x|^{-pb}|u|^{p-2}u\;\; \text{in } \mathbb R^N, \end{align*} where $h(x)\geq 0$, $f(x)$ is a continuous function which may change sign, $λ, μ$ are positive real parameters and $1 0$. Using the idea {of the constrained minimization on} Nehari manifold we show the existence of at least two positive solutions for suitable choices of $λ$ and $μ$.

math.AP↗

arXiv2018

Fractional Hamiltonian systems with critical exponential growth

In this paper, we study the following nonlocal nonautonomous Hamiltonian system on whole $\mathbb R$ $$ \left\{\begin{array}{ll} (-Δ)^\frac12~ u +u=Q(x) g(v)&\quad\mbox{in } \mathbb R,\\ (-Δ)^\frac12~ v+v = P(x)f(u)&\quad\mbox{in } \mathbb R, \end{array}\right. $$ where $(-Δ)^\frac12$ is {the} square root Laplacian operator. We assume that the nonlinearities $f, g$ have critical growth at $+\infty$ in the sense of Trudinger-Moser inequality and the nonnegative weights $P(x)$ and $Q(x)$ vanish at $+\infty$. Using suitable variational method combined with {the} generalized linking theorem, we obtain the existence of {at least one} positive solution for the above system.

math.AP↗