Electron. J. Differential Equations, Vol. 2022 (2022), No. 77, pp. 1-15.

Kirchhoff systems involving fractional p-Laplacian and singular nonlinearity

Mouna Kratou

In this work we consider the fractional Kirchhoff equations with singular nonlinearity,

where Ω is a bounded domain in RN with smooth boundary, N> ps, s in (0,1), 0<α<1, 0< β< 1, 2-α-β<p≤ pθ<q<p*s, p*s=2N/(N-2s) is the fractional Sobolev exponent, λ, μ are two parameters, a, b, c in C(overlineΩ) are non-negative weight functions, M(t)=k+ltθ-1 with k>0, l,θ≥1, and (-Δ)sp is the fractional p-laplacian operator. We prove the existence of multiple non-negative solutions by studying the nature of the Nehari manifold with respect to the parameters λ and μ.

Submitted September 11, 2022. Published November 21, 2022.
Math Subject Classifications: 34B15, 37C25, 35R20.
Key Words: Kirchhoff-type equations; fractional p-Laplace operator; Nehari manifold; singular elliptic system; multiple positive solutions,

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Mouna Kratou
College of sciences at Dammam
University of Imam Abdulrahman Bin Faisal
31441 Dammam, Saudi Arabia
email: mmkratou@iau.edu.sa

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