NONLINEAR WEIGHTED p-LAPLACIAN ELLIPTIC INEQUALITIES WITH GRADIENT TERMS
2010 ◽
Vol 12
(03)
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pp. 501-535
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Keyword(s):
In this paper, we give sufficient conditions for the existence and nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div {g(|x|)|Du|p-2Du} ≥ h(|x|)f(u)ℓ(|Du|). We achieve our conclusions by using a generalized version of the well-known Keller–Ossermann condition, first introduced in [2] for the generalized mean curvature case, and in [11, Sec. 4] for the nonweighted p-Laplacian equation. Several existence results are also proved in Secs. 2 and 3, from which we deduce simple criteria of independent interest stated in the Introduction.
1995 ◽
Vol 20
(1-2)
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pp. 233-265
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2003 ◽
Vol 16
(4)
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pp. 439-447
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2019 ◽
Vol 2019
(750)
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pp. 97-121
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1989 ◽
Vol 65
(7)
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pp. 207-210
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