On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms

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Abstract

In this paper we give sufficient conditions for the 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 |) | D u |p - 2 D u} ≥ h (| x |) f (u) ± over(h, ̃) (| x |) ℓ (| D u |), under the main request that h and over(h, ̃) are continuous on R+. We achieve our conclusions introducing a generalized version of the well-known Keller-Osserman condition. © 2009 Elsevier Inc. All rights reserved.

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Filippucci, R., Pucci, P., & Rigoli, M. (2009). On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms. Journal of Mathematical Analysis and Applications, 356(2), 689–697. https://doi.org/10.1016/j.jmaa.2009.03.050

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