论文信息 - Principal eigenvalues for problems with indefinite weight function on RN

Principal eigenvalues for problems with indefinite weight function on RN

We investigate the existence of positive principal eigenvalues of the problem −Δu(x)=λg(x)u for x∈R n ; u(x)→0 as x→∞ where the weight function g changes sign on R n . It is proved that such eigenvalues exist if g is negative and bounded away from 0 to ∞ or if n≥3 and |g(x)| is sufficiently small at ∞ but do not exist if n=1 or 2 and ∫ Rn g (x)dx>0

K. J. Brown | C. Cosner | J. Fleckinger

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