Positive solution branch for elliptic problems with critical indefinite nonlinearity

Giacomoni, Jacques ; Prajapat, J. ; Ramaswamy, Mythily (2005) Positive solution branch for elliptic problems with critical indefinite nonlinearity Differential and Integral Equations, 18 (7). pp. 721-764. ISSN 0893-4983

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Abstract

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely -Δu=λu+h(x)un+2/n-2 in a smooth domain bounded (respectively, unbounded) Ω⊆Rn, n>4, for λ≥0. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue λ1(Ω) (respectively, the bottom of the essential spectrum).

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Deposited On:20 Sep 2011 09:32
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