Some existence results of bounded variation solutions for a 1-biharmonic problem with vanishing potentials

Rui Liu; Lin Li; Donal O'Regan

doi:10.1002/mma.9234

Some existence results of bounded variation solutions for a 1-biharmonic problem with vanishing potentials

Rui Liu
, Lin Li
, Donal O'Regan

Mathematics

Chongqing Technology and Business University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

In this work, we study a quasilinear elliptic problem in the whole space (Figure presented.) involving the 1-biharmonic operator with potentials that can vanish at infinity. We consider two different geometrical assumptions in the nonlinearity and use variational methods to obtain nontrivial bounded variation solutions.

Original language	English
Pages (from-to)	13090-13102
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	12
DOIs	https://doi.org/10.1002/mma.9234
Publication status	Published - Aug 2023

Keywords

1-biharmonic operator
mountain pass theorem
variational methods

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title = "Some existence results of bounded variation solutions for a 1-biharmonic problem with vanishing potentials",

abstract = "In this work, we study a quasilinear elliptic problem in the whole space (Figure presented.) involving the 1-biharmonic operator with potentials that can vanish at infinity. We consider two different geometrical assumptions in the nonlinearity and use variational methods to obtain nontrivial bounded variation solutions.",

keywords = "1-biharmonic operator, mountain pass theorem, variational methods",

author = "Rui Liu and Lin Li and Donal O'Regan",

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AU - Li, Lin

AU - O'Regan, Donal

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N2 - In this work, we study a quasilinear elliptic problem in the whole space (Figure presented.) involving the 1-biharmonic operator with potentials that can vanish at infinity. We consider two different geometrical assumptions in the nonlinearity and use variational methods to obtain nontrivial bounded variation solutions.

AB - In this work, we study a quasilinear elliptic problem in the whole space (Figure presented.) involving the 1-biharmonic operator with potentials that can vanish at infinity. We consider two different geometrical assumptions in the nonlinearity and use variational methods to obtain nontrivial bounded variation solutions.

KW - 1-biharmonic operator

KW - mountain pass theorem

KW - variational methods

UR - https://www.scopus.com/pages/publications/85150997118

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DO - 10.1002/mma.9234

M3 - Article

AN - SCOPUS:85150997118

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 12

ER -

Some existence results of bounded variation solutions for a 1-biharmonic problem with vanishing potentials

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