arXiv subjects

Marcelo C. Ferreira

Publications and source records attributed to Marcelo C. Ferreira.

5 recordsLinked to original sources

arXiv2020

A nonhomogeneous critical Kirchhoff-Schrödinger type equation in $\mathbb{R}^{4}$ involving vanishing potentials

In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schrödinger type problem in $\mathbb R^4$ involving a critical nonlinearity and a suitable small perturbation. The arisen competition between the terms due to the nonlocal coefficient and critical nonlinearity turns out to be rather interesting. The main tools used in the present work are variational methods and the Lions' Concentration Compactness Principle.

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arXiv2019

Ground state solutions for a nonlocal equation in $\mathbb{R}^2$ involving vanishing potentials and exponential critical growth

In this paper, we study the following class of nonlinear equations: $$ -Δu+V(x) u = \left[|x|^{-μ}*(Q(x)F(u))\right]Q(x)f(u),\quad x\in\mathbb{R}^2, $$ where $V$ and $Q$ are continuous potentials, which can be unbounded or vanishing at infintiy, $f(s)$ is a continuous function, $F(s)$ is the primitive of $f(s)$, $*$ is the convolution operator and $0<μ<2$. Assuming that the nonlinearity $f(s)$ has exponential critical growth, we establish the existence of ground state solutions by using variational methods. For this, we prove a new version of the Trudinger-Moser inequality for our setting, which was necessary to obtain our main results.

math.AP↗

arXiv2014

Multi-bump solutions for a class of quasilinear problems involving variable exponents

We establish the existence of multi-bump solutions for the following class of quasilinear problems $$ - Δ_{ p(x) } u + \big( λV(x) + Z(x) \big) u ^{ p(x)-1 } = f(x,u) \text{ in } \mathbb R^N, \, u \ge 0 \text{ in } \mathbb R^N, $$ where the nonlinearity $ f \colon \mathbb R^N \times \mathbb R \to \mathbb R $ is a continuous function having a subcritical growth and potentials $ V, Z \colon \mathbb R^N \to \mathbb R $ are continuous functions verifying some hypotheses. The main tool used is the variational method.

math.AP↗

arXiv2013

Existence of solutions for a class of $p(x)$-laplacian equations involving a concave-convex nonlinearity with critical growth in $\mathbb{R}^{N}$

We prove the existence of solutions for a class of quasilinear problems involving variable exponents and with nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Principle and the Mountain Pass Theorem.

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arXiv2013

Nonlinear perturbations of a $p(x)$-Laplacian equation with critical growth in $\mathbb{R}^N$

We prove the existence of solution for a class of $p(x)$-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.

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