Korean Journal of Mathematics

  • 제17권4호
  • /
  • Pages.461-471
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  • 2009
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지

PALAIS-SMALE CONDITION FOR THE STRONGLY DEFINITE FUNCTIONAL

  • Jung, Tacksun (Department of Mathematics Kunsan National University) ;
  • Choi, Q-Heung (Department of Mathematics Education Inha University)
  • 투고 : 2009.10.12
  • 발행 : 2009.12.30
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초록

Let ${\Omega}$ be a bounded subset of $R^n$ with smooth boundary and H be a Sobolev space $W_0^{1,2}({\Omega})$. Let $I{\in}C^{1,1}$ be a strongly definite functional defined on a Hilbert space H. We investigate the conditions on which the functional I satisfies the Palais-Smale condition. Palais-Smale condition is important for determining the critical points for I by applying the critical point theory.

키워드

참고문헌

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  4. P. H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, C.B.M.S. Reg. Conf. Ser. in Math. 6, American Mathematical Society, Providence, R1,(1986).