Acta mathematica scientia,Series B ›› 1990, Vol. 10 ›› Issue (2): 121-134.

• Articles •     Next Articles

EXISTENCE OF NONTRIVIAL SOLUTION OF QUASILINEAR ELLIPTIC EIGENVALUE PROBLEM ON Rn WITH NATURAL GROWTH CONDITIONS

Yan Shusen, Li Gongbao   

  1. Inst. of Math. Sci., Academia Sinica, Wuhan, China
  • Received:1988-12-31 Online:1990-06-25 Published:1990-06-25
  • Supported by:
    This work is supported by the Youth Foundation, NSFC.

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Abstract: In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem
-Di(aij(u)Dju)+(1)/2aiju(u)DiuDju+hu=λ|u|p-2u,x∈Rn,u∈H1(Rn)∩L∞(Rn) with natural growth conditions.

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