Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction
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Abstract In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒ p , q M u := - Δ u + u p - M | ∇ u | q = μ {{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M|\nabla u|^{q}=\mu} in a domain Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} where μ is a nonnegative Radon measure, when p > 1 {p>1} , q > 1 {q>1} and M ≥ 0 {M\geq 0} . We also give conditions under which nonnegative solutions of ℒ p , q M u = 0 {{\mathcal{L}}^{{M}}_{p,q}u=0} in Ω ∖ K {\Omega\setminus K} , where K is a compact subset of Ω, can be extended as a solution of the same equation in Ω.
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2003 ◽
Vol 9
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pp. 88-93
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1976 ◽
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pp. 820-839
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pp. 293-298
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Multiple solutions for semi-linear corner degenerate elliptic equations with singular potential term
2016 ◽
Vol 19
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pp. 1650043
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Vol 10
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pp. 179-239
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