Existence and multiplicity of positive solutions for a class of singular Kirchhoff type problems with sign‐changing potential

Abstract

In this paper, the existence and multiplicity of positive solutions are obtained for a class of Kirchhoff type problems with two singular terms and sign‐changing potential by the Nehari method.

A uniqueness positive solutions for strong singular Kirchhoff-type fractional Laplacian problems with Hardy term

“…Since then, a great deal of work has been devoted to Kirchhoff-type fractional Laplacian problems. The singular Kirchhoff type problem was firstly investigated by Liu and Sun [3], they obtain two positive solutions with the help of the Nehari method. Li, Tang and Liao in [2] and [3] Ω is nonzero and nonnegative, Liao in [4] explore the two solutions of a class of singular Kirchhoff-type problems with Hardy-Sobolev critical exponent II * .…”

“…The singular Kirchhoff type problem was firstly investigated by Liu and Sun [3], they obtain two positive solutions with the help of the Nehari method. Li, Tang and Liao in [2] and [3] Ω is nonzero and nonnegative, Liao in [4] explore the two solutions of a class of singular Kirchhoff-type problems with Hardy-Sobolev critical exponent II * . Concerning the existence theorems for entire solutions of stationary Kirchhoff Fractional p-Laplace equation with Hardy term, see [5].…”

Two solutions for a class of singular Kirchhoff‐type problems with Hardy–Sobolev critical exponent II

“…(Ω) is nonzero and nonnegative, Li et al 3 generalized Liu and Sun 2 to problem (1.2) with 0 ≤ s < 1, p = 3. When s = 0, Lei et al studied the critical case of problem (1.2) with p = 5, = g(x) ≡ 1 and obtained two positive solutions by using the variational method and perturbation method 4 ; the case of p = 3 is considered in Liao et al 5 The first work on the Kirchhoff-type problem with critical Sobolev exponent is Alves et al 6 After that, the Kirchhoff-type equation with critical exponent has been extensively studied, and some important and interesting results have been obtained, for example, previous studies.…”

“…By the Nehari method, when λ >0 small, they obtained two positive solutions for problem (). When g ∈ L ∞ (Ω) may change sign in Ω and is nonzero and nonnegative, Li et al 3 generalized Liu and Sun 2 to problem () with 0 ≤ s <1, p =3. When s =0, Lei et al studied the critical case of problem () with p =5, λ = g ( x )≡1 and obtained two positive solutions by using the variational method and perturbation method 4 ; the case of p =3 is considered in Liao et al 5 …”