arXiv subjects

Lais Santos

Publications and source records attributed to Lais Santos.

3 recordsLinked to original sources

arXiv2021

Multiplicity for a strongly singular quasilinear problem via bifurcation theory

A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence of an unbounded branch of positive solutions, which is bounded in positive $λ-$direction and bifurcates from infinity at $λ=0$. As consequence of the bifurcation result, we determine intervals of existence, nonexistence and, in particular cases, global multiplicity.

math.AP↗

arXiv2019

Equivalent conditions for existence of three solutions for a problem with discontinuous and strongly-singular terms

In this paper, we are concerned with a Kirchhoff problem in the presence of a strongly-singular term perturbed by a discontinuous nonlinearity of the Heaviside type in the setting of Orlicz-Sobolev space. The presence of both strongly-singular and non-continuous terms bring up difficulties in associating a differentiable functional to the problem with finite energy in the whole space $W_0^{1,Φ}(Ω)$. To overcome this obstacle, we established an optimal condition for the existence of $W_0^{1,Φ}(Ω)$-solutions to a strongly-singular problem, which allows us to constrain the energy functional to a subset of $W_0^{1,Φ}(Ω)$ to apply techniques of convex analysis and generalized gradient in Clarke sense.

math.AP↗

arXiv2018

Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term

In this paper, we show existence of \textit{continuums} of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in $\mathbb{R}^N$ with $N \geq 2$. We approached non-autonomous and non-local equations by applying the Bifurcation Theory to the corresponding $ε$-perturbed problems and using a comparison principle for $W_{\mathrm{loc}}^{1,p}(Ω)$-sub and supersolutions to obtain qualitative properties of the $ε$-\textit{continuum} limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous Kirchhoff problem to get the existence of a \textit{continuum} of positive solutions.

math.AP↗