On semilinear elliptic equations with diffuse measures
نویسندگان
چکیده
منابع مشابه
Semilinear fractional elliptic equations involving measures
We study the existence of weak solutions to (E) (−∆)u+g(u) = ν in a bounded regular domain Ω in R (N ≥ 2) which vanish in R \Ω, where (−∆) denotes the fractional Laplacian with α ∈ (0, 1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of a weak solution for pr...
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We study the existence of solutions to the fractional elliptic equation (E1) (−∆)u + ǫg(|∇u|) = ν in a bounded regular domain Ω of R (N ≥ 2), subject to the condition (E2) u = 0 in Ω, where ǫ = 1 or −1, (−∆) denotes the fractional Laplacian with α ∈ (1/2, 1), ν is a Radon measure and g : R+ 7→ R+ is a continuous function. We prove the existence of weak solutions for problem (E1)-(E2) when g is ...
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A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.
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We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...
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ژورنال
عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA
سال: 2018
ISSN: 1021-9722,1420-9004
DOI: 10.1007/s00030-018-0526-6