Qi Li, Yuzhu Han, Jian Wang
Abstract:
This article studies a perturbed critical biharmonic equation with Hardy potential.
The main challenge arises from the combined effects of critical Sobolev nonlinearity
and singular Hardy potential, which induce a double loss of compactness in the
variational framework. Through delicate analysis of fibering maps and the mountain
pass lemma, the existence of at least one nontrivial mountain pass solution is
obtained under appropriate growth conditions on the nonlinearity.
Submitted April 6, 2026. Published April 28, 2026.
Math Subject Classifications: 35J35, 35J91.
Key Words: Biharmonic equation; critical exponent; mountain pass lemma; Hardy term.
DOI: 10.58997/ejde.2026.30
Show me the PDF file (387 KB), TEX file for this article.
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Qi Li School of Mathematical Sciences Dalian Minzu University Dalian 116600, China email: 20231577@dlnu.edu.cn |
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Yuzhu Han School of Mathematics Jilin University Changchun 130012, China email: yzhan@jlu.edu.cn |
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Jian Wang School of Mathematical Sciences Ocean University of China Qingdao 266100, China email: pdejwang@ouc.edu.cn |
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