Akkoyunlu, Ebubekir; Ayazoglu, Rabil

In the present paper, we investigate the existence of multiple solutions for the nonhomogeneous fractional p-Kirchhoff equation M(∬R2N|u(x)-u(y)|p|x-y|N+psdxdy+∫RNV(x)|u|pdx)×((-Δ)psu+V(x)|u|p-2u)=f(x,u)inRN,where (-Δ)ps is the fractional p-Laplacian operator, 0 < s< 1 < p< ∞ with sp< N, M:R0+→R0+ is a nonnegative, continuous and increasing Kirchhoff function, the nonlinearity f: RN× R→ R is a Carathéodory function that obeys some conditions which will be stated later and V∈ C(RN, R+) is a non-negative potential function. We first establish the Bartsch–Pankov–Wang type compact embedding theorem for the fractional Sobolev spaces. Then multiplicity results are obtained by using the variational method, (S+) mapping theory and Krasnoselskii’s genus theory.

AtıfScopus4·WoS4

İncele

Ayazoglu, Rabil; Hasanov, Javanshir J.

We consider the generalized shift operator associated with the Laplace-Bessel differential operator Δ B = i=1 n 2 x i 2 +i=1 k γ i x ix i .Δ -B=Σ -i=1ⁿ(∂ ²)/(∂ x-i²) +Σ -i=1^k (γ -i)/(x-i)(∂)/(∂ x-i). The maximal operator M γ M-γ (B-maximal operator) and the Riesz potential I α,γ I-α ,γ (B-Riesz potential), associated with the generalized shift operator are investigated. We prove that the B-maximal operator M γ M-γ and the B-singular integral operator are bounded from the generalized weighted B-Morrey space p,ω 1 ,φ,γ (k,+ n )cal M-p,ω -1,φ ,γ (ℝ-k,+ⁿ) to p,ω 2 ,φ,γ (k,+ n )cal M-p,ω -2,φ ,γ (ℝ-k,+ⁿ) for all 1<p<1 &lt; p &lt; ∞ , φA p,γ (k,+ n )φ ∈ A-p,γ (ℝ-k,+ⁿ) . Furthermore, we prove that the B-Riesz potential I α,γ I-α ,γ , 0<α<n+|γ|0&lt;α &lt;n+|γ | , is bounded from the generalized weighted B-Morrey space p,ω 1 ,φ,γ (k,+ n )cal M-p,ω -1,φ ,γ (ℝ-k,+ⁿ) to q,ω 2 ,φ,γ (k,+ n )cal M-q,ω -2,φ ,γ (ℝ-k,+ⁿ) , where α/(n+|γ|)=1/p-1/qα /(n+|γ |)=1/p-1/q , 1<p<(n+|γ|)/α1&lt;p&lt;(n+|γ |)/α , φA 1+q/p ' ,γ (k,+ n )φ ∈ A-1+q/p^′,γ (ℝ-k,+ⁿ) and 1/p+1/p ' =11/p+1/p^′=1 .

AtıfScopus2·WoS2·OpenAlex2

İncele