Existence of solutions for some nonlinear elliptic equations
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In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset Ω of ℝN:
-Δpu = ƒ(x, u, ∇u) + μ in Ω,
u = 0 on ∂Ω,
where μ is a Radon measure on Ω which is zero on sets of p-capacity zero, ƒ : Ω x ℝ x ℝN → ℝ is a Carathéodory function that satisfies certain conditions with respect to the one dimensional spectrum.
CitationAnane, A., Chakrone, O., & Chehabi, M. (2006). Existence of solutions for some nonlinear elliptic equations. Electronic Journal of Differential Equations, 2006(63), pp. 1-13.
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