Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>

Chen, Shaoxiong; Liu, Jiu; Wang, Xian

doi:10.1016/j.amc.2014.10.021

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Cited by 18 publications

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“…To overcome the lack of compactness, the condition (V) , which was first introduced by Bartsch and Wang in [5], is always assumed to preserve the compactness of embedding of the working space. From [11], we know that under the assumption (H1), the continuous embedding…”

Section: Introductionmentioning

confidence: 99%

Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities

Meng,

Zhang,

Zhang

2020

ejde

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In this article, we study the multiplicity of positive solutions for the biharmonic equation of Kirchhoff type involving concave-convex nonlinearities, $$ \Delta^2u-\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\Big)\Delta u+V(x)u =\lambda f_1(x)|u|^{q-2}u+f_2(x)|u|^{p-2}u. $$ Using the Nehari manifold, Ekeland variational principle, and the theory of Lagrange multipliers, we prove that there are at least two positive solutions, one of which is a positive ground state solution. For more information see https://ejde.math.txstate.edu/Volumes/2020/44/abstr.html

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Section: Introductionmentioning

confidence: 99%