Low perturbations and combined effects of critical and singular nonlinearities in Kirchhoff problems
type: Item
instance of: scholarly article
title: Low perturbations and combined effects of critical and singular nonlinearities in Kirchhoff problems
zbMATH Open document ID: 1504.35146
author: Chun-Yu Lei
author: Vicenţiu D. Rădulescu
author: Binlin Zhang
published in: Applied Mathematics and Optimization
publication date: 2022-11-11T00:00:00Z
review text: Given a bounded domain \(\Omega \subset \mathbb{R}^3\) with smooth boundary \(\partial\Omega\), this paper is concerned with Kirchhoff problems involving critical growth and singular terms given by \[ \begin{cases} -\left(a+b\displaystyle \int_\Omega |\nabla u|^2\,\mathrm{d}x\right)\Delta u=\lambda u^{-\gamma}+u^5,\quad &\text{in }\Omega,\\ u>0&\text{in }\Omega,\\ u=0,&\text{on }\partial\Omega, \end{cases} \] where \(\gamma \in (0,1)\), \(a\), \(b\) are positive constants, \(\lambda>0\) is a parameter and \(\Delta\) denotes the Laplacian. Applying variational methods, the authors prove the existence of at least two positive solutions provided the parameter \(\lambda>0\) is sufficiently small.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J62
zbMATH DE Number: 7615105
zbMATH Keywords: Kirchhoff equation
zbMATH Keywords: critical growth
zbMATH Keywords: singular nonlinearity
zbMATH Keywords: multiple positive solutions
zbMATH Keywords: Ekeland's variational principle
MaRDI profile type: Publication
full work available at URL: s00245-022-09913-9
OpenAlex ID: W4308459228
cites work: Dual variational methods in critical point theory and applications
cites work: Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
cites work: The elliptic Kirchhoff equation in \(\mathbb {R}^{N}\) perturbed by a local nonlinearity.
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Q4860444
cites work: The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions
cites work: Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity
cites work: On a dirichlet problem with a singular nonlinearity
cites work: Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in \(\mathbb{R}^3\)
cites work: Q3726641
cites work: On the variational principle
cites work: Q3276827
cites work: Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument
cites work: Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
cites work: On Kirchhoff type equations with critical Sobolev exponent
cites work: Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities
cites work: Metric critical point theory. I: Morse regularity and homotopic stability of a minimum
cites work: Positive solutions for a Kirchhoff problem with vanishing nonlocal term
cites work: Mountain pass theorems and global homeomorphism theorems
cites work: Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
cites work: Existence of a positive solution to Kirchhoff-type problems without compactness conditions
cites work: Uniqueness theorems through the method of moving spheres
cites work: Critical point theory for nonsmooth functionals
cites work: Variational Methods for Nonlocal Fractional Problems
cites work: Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems
cites work: A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
cites work: The critical problem of Kirchhoff type elliptic equations in dimension four
cites work: Nontrivial solutions of Kirchhoff-type problems via the Yang index
cites work: The existence of minimal immersions of 2-spheres
cites work: Ekeland's variational principle and the mountain pass lemma
cites work: A nonlinear singular boundary value problem
cites work: Q3419565
cites work: Existence and multiplicity of solutions for critical Kirchhoff-type \(p\)-Laplacian problems
cites work: A uniqueness result for strong singular Kirchhoff-type fractional Laplacian problems
cites work: Q3275400
DOI: 10.1007/S00245-022-09913-9
description: scientific article; zbMATH DE number 7615105