In this paper, we consider the following critical nonlocal problem: (equation presented). where ω is an open bounded subset of ℝN with continuous boundary, dimension N > 2s with parameter s ϵ (0, 1), 2.s = 2N/(N - 2s) is the fractional critical Sobolev exponent, λ > 0 is a real parameter, γ ϵ (0, 1) and M models a Kirchhoff-type coefficient, while (-δ) s is the fractional Laplace operator. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. By combining variational methods with an appropriate truncation argument, we provide the existence of two solutions.
Fiscella, A. (2019). A fractional Kirchhoff problem involving a singular term and a critical nonlinearity. ADVANCES IN NONLINEAR ANALYSIS, 8(1), 645-660 [10.1515/anona-2017-0075].
A fractional Kirchhoff problem involving a singular term and a critical nonlinearity
Fiscella A
2019
Abstract
In this paper, we consider the following critical nonlocal problem: (equation presented). where ω is an open bounded subset of ℝN with continuous boundary, dimension N > 2s with parameter s ϵ (0, 1), 2.s = 2N/(N - 2s) is the fractional critical Sobolev exponent, λ > 0 is a real parameter, γ ϵ (0, 1) and M models a Kirchhoff-type coefficient, while (-δ) s is the fractional Laplace operator. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. By combining variational methods with an appropriate truncation argument, we provide the existence of two solutions.
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