Existence and uniqueness of positive solution for \(p\)-Laplacian Kirchhoff-Schrödinger-type equation
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive solution for \(p\)-Laplacian Kirchhoff-Schrödinger-type equation
zbMATH Open document ID: 1440.35108
DOI: 10.1155/2018/9096260
author: Wei Han
author: Jiangyan Yao
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We study the existence and uniqueness of positive solution for the following \(p\)-Laplacian-Kirchhoff-Schrödinger-type equation: \(\left\{- \left(a + b \int_\Omega | \nabla u|^p\right) \Delta_p u + \lambda v \left(x\right) | u| ^{p - 2} u = h f \left(u\right) - \mu g \left(u\right), \text{ in } \Omega, \quad u > 0, \text{ in } \Omega,\quad u = 0, \text{ on } \partial \Omega\right\}\), where \(\Omega \subset R^N\) \((N \geq 3)\), \(\lambda, \mu \geq 0\) are parameters, \(v(x)\), \(f(u)\), \(g(u)\) and \(h\) are under some suitable assumptions. For the purpose of overcoming the difficulty caused by the appearance of the Schrödinger term and general singularity, we use the variational method and some mathematical skills to obtain the existence and uniqueness of the solution to this problem.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6992037
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/9096260
OpenAlex ID: W2805253683
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description: scientific article; zbMATH DE number 6992037