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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.12 No.4
- 발행연도
- 2008.12
- 수록면
- 239 - 247 (9page)
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Let I ∈ C<SUP>1,1</SUP> be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m (m≥2) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with (P.S.)<SUP>*</SUP><SUB>c</SUB> condition. Moreover we show that I has at least 2m critical points when I satisfies m (m≥2) pairs of Torus-Sphere variational linking inequalities with (P.S.)<SUP>*</SUP><SUB>c</SUB> condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.
목차
ABSTRACT
1. INTRODUCTION AND STATEMENT OF THE MAIN RESULTS
2. CRITICAL POINT THEORY ON THE MANIFOLD WITH BOUNDARY
3. PROOF OF THEOREM 1.1
4. PROOF OF THEOREM 1.2
REFERENCES
참고문헌 (8)
참고문헌 신청
정택선 / 2008 / THE NUMBER OF THE CRITICAL POINTS OF THE STRONGLY INDEFINITE FUNCTIONAL WITH ONE PAIR OF THE TORUS-SPHERE VARIATIONAL LINKING SUBLEVELS / 한국수학논문집 16(4):527~535
G. Fournier / 1993 / Limit relative category and ctritical point theory / Dynam. Report 3:1~23
D. Lupo / 1996 / Two applications of a three critical points theorem / J. Differential Equations 132:222~238
A. Marino / 1991 / Same variational results on semilinear problems with asymptoticallly nonsymmetric behaviour, Nonlinear Analysis / A Tribute in honour of G. Pordi”, S.U.S. Pisa
A. Marino / 1994 / A nonsymmetric asymptotically linear elliptic problem / Topol. Meth. Nonlin. Anal 4:289~339
G. Fournier / 1993 / Limit relative category and ctritical point theory / Dynam. Report 3:1~23
D. Lupo / 1996 / Two applications of a three critical points theorem / J. Differential Equations 132:222~238
A. Marino / 1991 / Same variational results on semilinear problems with asymptoticallly nonsymmetric behaviour, Nonlinear Analysis / A Tribute in honour of G. Pordi”, S.U.S. Pisa
A. Marino / 1994 / A nonsymmetric asymptotically linear elliptic problem / Topol. Meth. Nonlin. Anal 4:289~339
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UCI(KEPA) : I410-ECN-0101-2009-410-015704177