Remarks on the clark theorem

Guosheng Jiang; Kazunaga Tanaka; Chengxiang Zhang

Remarks on the clark theorem

Guosheng Jiang, Kazunaga Tanaka^*, Chengxiang Zhang

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to 0 and it has important applications to sublinear elliptic problems. We study the convergence of the corresponding critical points and we give a characterization of accumulation points of critical points together with examples, in which critical points with negative critical values converges to nonzero critical point. Our results improve the abstract results in Kajikiya [4] and Liu-Wang [7].

Original language	English
Pages (from-to)	1421-1434
Number of pages	14
Journal	Journal of Nonlinear and Convex Analysis
Volume	18
Issue number	8
Publication status	Published - 2017

Keywords

Clark theorem
Genus
Minimax method

ASJC Scopus subject areas

Analysis
Geometry and Topology
Control and Optimization
Applied Mathematics

Cite this

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title = "Remarks on the clark theorem",

abstract = "The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to 0 and it has important applications to sublinear elliptic problems. We study the convergence of the corresponding critical points and we give a characterization of accumulation points of critical points together with examples, in which critical points with negative critical values converges to nonzero critical point. Our results improve the abstract results in Kajikiya [4] and Liu-Wang [7].",

keywords = "Clark theorem, Genus, Minimax method",

author = "Guosheng Jiang and Kazunaga Tanaka and Chengxiang Zhang",

note = "Funding Information: Authors started this research during the first and the third authors{\textquoteright} visit to Department of Mathematics, School of Science and Engineering, Waseda University from Capital Normal University and Nankai University. They would like to gratefully acknowledge Waseda University for cordial invitations and hospitality. The first author wishes to express his gratitude to the support of Graduate School of Capital Normal University. The third author is greatly indebted to China Scholarship Council for their support. Publisher Copyright: {\textcopyright} Copyright 2017.",

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AU - Jiang, Guosheng

AU - Tanaka, Kazunaga

AU - Zhang, Chengxiang

N1 - Funding Information: Authors started this research during the first and the third authors’ visit to Department of Mathematics, School of Science and Engineering, Waseda University from Capital Normal University and Nankai University. They would like to gratefully acknowledge Waseda University for cordial invitations and hospitality. The first author wishes to express his gratitude to the support of Graduate School of Capital Normal University. The third author is greatly indebted to China Scholarship Council for their support. Publisher Copyright: © Copyright 2017.

PY - 2017

Y1 - 2017

N2 - The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to 0 and it has important applications to sublinear elliptic problems. We study the convergence of the corresponding critical points and we give a characterization of accumulation points of critical points together with examples, in which critical points with negative critical values converges to nonzero critical point. Our results improve the abstract results in Kajikiya [4] and Liu-Wang [7].

AB - The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to 0 and it has important applications to sublinear elliptic problems. We study the convergence of the corresponding critical points and we give a characterization of accumulation points of critical points together with examples, in which critical points with negative critical values converges to nonzero critical point. Our results improve the abstract results in Kajikiya [4] and Liu-Wang [7].

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KW - Minimax method

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Remarks on the clark theorem

Abstract

Keywords

ASJC Scopus subject areas

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