Monotone perturbations of the laplacian inL
1(R
N
) |
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Authors: | Juan Luis Vázquez |
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Institution: | (1) División de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain |
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Abstract: | The semilinear perturbation of Poisson’s equation (E): −Δu+β(u)∋f, where β is a maximal monotone graph inR, has been investigated by Ph. Bénilan, H. Brézis and M. Crandall forf∈L
1(R
N
),N≧1, under the assumptions 0∈β(0) ifN≧3 and 0∈β(0) ∩ Int β(R) ifN=1,2. We discuss in this paper the solvability and well-posedness of (E) in terms of any maximal monotone graph β. In particular,
if β takes only positive values andN≧3 we prove that no solution exists; ifN=2 we give necessary and sufficient conditions on β andf for (E) to be solvable in a natural sense. |
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Keywords: | |
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