In the present paper, we study the following singular Kirchhoff problem [Formula presented], where Ω⊂RN is an open bounded domain, dimension N>2s with s∈(0,1), 2s ∗=2N∕(N−2s) is the fractional critical Sobolev exponent, parameter λ>0, exponent γ∈(0,1), M models a Kirchhoff coefficient, [Formula presented] is a positive weight, while g∈L∞(Ω) is a sign-changing function. Using the idea of Nehari manifold technique, we prove the existence of at least two positive solutions for a sufficiently small choice of λ. This approach allows us to avoid any restriction on the boundary of Ω.

Fiscella, A., Mishra, P. (2019). The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms. NONLINEAR ANALYSIS, 186, 6-32 [10.1016/j.na.2018.09.006].

The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms

Fiscella A
;
2019

Abstract

In the present paper, we study the following singular Kirchhoff problem [Formula presented], where Ω⊂RN is an open bounded domain, dimension N>2s with s∈(0,1), 2s ∗=2N∕(N−2s) is the fractional critical Sobolev exponent, parameter λ>0, exponent γ∈(0,1), M models a Kirchhoff coefficient, [Formula presented] is a positive weight, while g∈L∞(Ω) is a sign-changing function. Using the idea of Nehari manifold technique, we prove the existence of at least two positive solutions for a sufficiently small choice of λ. This approach allows us to avoid any restriction on the boundary of Ω.
Articolo in rivista - Articolo scientifico
Kirchhoff type problems, fractional Laplacian, singularities, critical nonlinearities, Nehari manifolds
English
6
32
27
Fiscella, A., Mishra, P. (2019). The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms. NONLINEAR ANALYSIS, 186, 6-32 [10.1016/j.na.2018.09.006].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/338114
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