A Semilinear Dirichlet Problem
1979 ◽
Vol 31
(2)
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pp. 337-340
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Keyword(s):
Introduction and notations. Let Ω be a bounded region in Rn. In this note we discuss the existence of weak solutions (see [4, Section 2]) of the Dirichlet problem(I)where Δ is the Laplacian operator, g : Ω × R → R and f : Ω × Rn+1 → R are functions satisfying the Caratheodory condition (see [2, Section 3]), and ∇ is the gradient operator.We let λ1 < λ2 ≦ … ≦ λm ≦ … denote the sequence of numbers for which the problem(II)has nontrivial weak solutions.
2016 ◽
Vol 15
(05)
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pp. 607-640
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Keyword(s):
1989 ◽
Vol 113
(1-2)
◽
pp. 149-158
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2016 ◽
Vol 1
(1)
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pp. 8-17