Twin positive solutions for Schrödinger-Kirchhoff-type problem with singularity and critical exponents
type: Item
instance of: scholarly article
title: Twin positive solutions for Schrödinger-Kirchhoff-type problem with singularity and critical exponents
zbMATH Open document ID: 1454.35139
DOI: 10.1155/2018/6108538
author: Wei Han
author: Yangyang Zhao
published in: Journal of Function Spaces
publication date: 2018-05-15T00:00:00Z
review text: Summary: We study in this paper the following singular Schrödinger-Kirchhoff-type problem with critical exponent \(-(a + b \int_{\Omega}|\nabla u|^2 dx)\Delta u + u = Q(x) u^5 + \mu|x|^{\alpha - 2} u + f(x)(\lambda / u^\gamma)\) in \(\Omega\), \(u = 0\) on \(\partial\Omega\), where \(a, b > 0\) are constants, \(\Omega \subset \mathbb R^3\) is a smooth bounded domain, \(0 < \alpha < 1\), \(\lambda > 0\) is a real parameter, \(\gamma \in(0,1)\) is a constant, and \(0 < \mu < a \mu_1\) (\(\mu_1\) is the first eigenvalue of \(-\Delta u = \mu|x|^{\alpha - 2} u\), under Dirichlet boundary condition). Under appropriate assumptions on \(Q\) and \(f\), we obtain two positive solutions via the variational and perturbation methods.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6868708
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6108538
OpenAlex ID: W2800599727
cites work: Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in \(\mathbb{R}^3\)
cites work: Infinitely many solutions for super-quadratic Kirchhoff-type equations with sign-changing potential
cites work: Positive solutions of logistic equations with dependence on gradient and nonhomogeneous Kirchhoff term
cites work: Ground state solution for a Kirchhoff problem with exponential critical growth
cites work: Energy functionals of Kirchhoff-type problems having multiple global minima
cites work: Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents
cites work: Q4189540
cites work: Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
cites work: Global solvability for the degenerate Kirchhoff equation with real analytic data
cites work: On the Well-Posedness of the Kirchhoff String
cites work: Nontrivial solutions of Kirchhoff-type problems via the Yang index
cites work: Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
cites work: The existence of a nontrivial solution to a nonlinear elliptic boundary value problem of \(p\)-Laplacian type without the Ambrosetti-Rabinowitz condition
cites work: Elliptic equations and systems with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition
cites work: N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition
cites work: Fractional \(p\)-Kirchhoff system with sign changing nonlinearities
cites work: Existence and multiplicity results for a \(p\)-Kirchhoff equation with a concave-convex term
cites work: On Kirchhoff type problems involving critical and singular nonlinearities
cites work: Existence of solutions to a class of semilinear elliptic equations involving general subcritical growth
cites work: On ground state solutions for a Kirchhoff type equation with critical growth
cites work: Ground state sign-changing solutions for asymptotically 3-linear Kirchhoff-type problems
cites work: Existence and multiplicity of solutions for Kirchhoff type problem with critical exponent
description: scientific article; zbMATH DE number 6868708