Existence and multiplicity for fractional differential equations with \(m(\xi )\)-Kirchhoff type-equation

• Acerbi E, Mingione G (2005) Gradient estimates for the \(p(x)\)-Laplacian system, pp 117–148

• Afrouzi GA, Mirzapour M (2013) Eigenvalue problems for \(p(x)\)-Kirchhoff type equations. Electron J Differ Equ 253:1–10

  MathSciNet  Google Scholar 

• Ambrosio V (2022) A Kirchhoff type equation in \({\mathbb{R} }^{N}\) involving the fractional \((p, q)\)-Laplacian. J Geom Anal 32(4):135

  Article  Google Scholar 

• Ambrosio V, Isernia T, Radulescu VD (2021) Concentration of positive solutions for a class of fractional \(p\)-Kirchhoff type equations. Proc R Soc Edinb Sect A Math 151(2):601–651

  Article  MathSciNet  Google Scholar 

• Antontsev S, Chipot M, Xiw Y (2007) Uniqueness results for equations of the \(p(x)\)-Laplacian type. Adv Math Sci Appl 17(1):287–304

  MathSciNet  Google Scholar 

• Applebaum D (2009) Levy processes and stochastic calculus, 2nd edn. Cambridge studies in advanced mathematics, vol 116. Cambridge University Press, Cambridge,

• Azroul E, Benkirane A, Shimi M, Srati M (2021) On a class of fractional \(p(x)\)-Kirchhoff type problems. Appl Anal 100(2):383–402

  Article  MathSciNet  Google Scholar 

• Binlin Z, Radulescu VD, Wang L (2019) Existence results for Kirchhoff-type superlinear problems involving the fractional Laplacian. Proc R Soc Edinb Sect A Math 149(4):1061–1081

  Article  MathSciNet  Google Scholar 

• Bouabdallah M, Chakrone O, Chehabi M, Jiabin Z (2023) Solvability of a nonlocal fractional p-Kirchhoff type problem. Rendiconti del Circolo Matematico di Palermo Series 2 72(8):3971–3985

  Article  MathSciNet  Google Scholar 

• Boudjeriou T (2020) On the diffusion \(p(x)\)-Laplacian with logarithmic nonlinearity. J Ellip Parabol Equ 6(2):773–794

  Article  MathSciNet  Google Scholar 

• Bucur C, Valdinoci E (2016) Nonlocal diffusion and applications, vol 1. Springer, Cham

  Book  Google Scholar 

• Byun S-S, Ok J (2016) On \(W^{1, q(\cdot )}\)-estimates for elliptic equations of \(p(x)\)-Laplacian type. J Math Pures Appl 106(3):512–545

  Article  MathSciNet  Google Scholar 

• Caffarelli L (2012) Nonlocal equations, drifts and games. Nonlinear Partial Differ Equ 7:37–52

  Article  MathSciNet  Google Scholar 

• Cen J, Vetro C, Zeng S (2023) A multiplicity theorem for double phase degenerate Kirchhoff problems. Appl Math Lett 146:108803

  Article  MathSciNet  Google Scholar 

• Chabrowski J, Fu Y (2005) Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain. J Math Anal Appl 306(2):604–618

  Article  MathSciNet  Google Scholar 

• Chen Y, Levine S, Rao M (2006) Variable exponent, linear growth functionals in image restoration. SIAM J Appl Math 66(4):1383–1406

  Article  MathSciNet  Google Scholar 

• Cont R, Tankov P (2004) Financial modelling with jump processes. Chapman & Hall/CRC Financial Mathematics Series, Boca Raton

  Google Scholar 

• Dai G, Ma R (2011) Solutions for a \(p(x)\)-Kirchhoff type equation with Neumann boundary data. Nonlinear Anal Real World Appl 12(5):2666–2680

  Article  MathSciNet  Google Scholar 

• Ebmeyer C, Liu WB (2008) Finite element approximation of the fast diffusion and the porous medium equations. SIAM J Numer Anal 46(5):2393–2410

  Article  MathSciNet  Google Scholar 

• Ezati R, Nyamoradi N (2021) Existence of solutions to a Kirchhoff \(\psi \)-Hilfer fractional \(p\)-Laplacian equations. Math Methods Appl Sci 44(17):12909–12920

  Article  MathSciNet  Google Scholar 

• Fan X (2011) Existence and uniqueness for the \(p(x)\)-Laplacian-Dirichlet problems. Math Nachric 284(11–12):1435–1445

  Article  MathSciNet  Google Scholar 

• Fan X-L, Zhang Q-H (2003) Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem. Nonlinear Anal 52(8):1843–1852

  Article  MathSciNet  Google Scholar 

• Gao Y, Luo X, Zhen M (2024) Existence and classification of positive solutions for coupled purely critical Kirchhoff system. Bull Math Sci 2024:2450002

  Article  MathSciNet  Google Scholar 

• Hamdani MK, Harrabi A, Mtiri F, Repovs DD (2020) Existence and multiplicity results for a new \(p(x)\)-Kirchhoff problem. Nonlinear Anal 190:111598

  Article  MathSciNet  Google Scholar 

• Horrigue S, Alsulami M, Alsaeedi BA (2023) Existence result to a Kirchhoff \(\psi \)-Hilfer fractional equations with \(p\)-Laplacian operator via Nehari method. In: 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE

• Lapa EC (2023) Global solutions for a nonlinear Kirchhoff type equation with viscosity. Opuscula Math 43:5

  Article  MathSciNet  Google Scholar 

• Laskin N (2000) Fractional quantum mechanics and Levy path integrals. Phys Lett A 268:298–305

  Article  MathSciNet  Google Scholar 

• Li Q, Han Y (2022) Existence and multiplicity of positive solutions to a \(p\)-Kirchhoff-type equation. Bull Malays Math Sci Soc 45(4):1789–1810

  Article  MathSciNet  Google Scholar 

• Liu Z, Motreanu D, Zeng S (2023) Multiple solutions for a Kirchhoff-type problem with vanishing nonlocal term and fractional \(p\)-Laplacian. Front Math 18(5):1067–1082

  Article  MathSciNet  Google Scholar 

• Lv P, Lin G, Lv X (2024) The asymptotic behaviors of solutions for higher-order \((m_1, m_2)\)-coupled Kirchhoff models with nonlinear strong damping. Demonstratio Math 56(1):20220197

  Article  MathSciNet  Google Scholar 

• Nezza D, Eleonora GP, Valdinoci E (2012) Hitchhiker’s guide to the fractional Sobolev spaces. Bull Sci Math 136(5):521–573

  Article  MathSciNet  Google Scholar 

• Pan N, Zhang B, Cao J (2016) Weak solutions for parabolic equations with \(p(x)\)-growth. Electron J Differ Equ 209:15

  MathSciNet  Google Scholar 

• Rajagopal KR, Ruzicka M (1996) On the modeling of electrorheological materials. Mech Res Commun 23(4):401–407

  Article  Google Scholar 

• Rajagopal KR, Ruzicka M (2001) Mathematical modeling of electrorheological materials. Contin Mech Thermodyn 13(1):59–78

  Article  Google Scholar 

• Rionero S (2013) Triple diffusive convection in porous media. Acta Mech 224(2):447–458

  Article  MathSciNet  Google Scholar 

• Rzymowski W (2002) One-dimensional Kirchhoff equation. Nonlinear Anal 48(2):209–221

  Article  MathSciNet  Google Scholar 

• Shibata T (2022) Bifurcation diagrams of one-dimensional Kirchhoff-type equations. Adv Nonlinear Anal 12(1):356–368

  Article  MathSciNet  Google Scholar 

• Sousa JVDC (2022) Existence and uniqueness of solutions for the fractional differential equations with \(p\)-Laplacian in \({\mathbb{H} }^{\nu,\eta; \psi }_{p}\). J Appl Anal Comput 12(2):622–661

  MathSciNet  Google Scholar 

• Sousa JVDC (2023) Fractional Kirchhoff-type systems via sub-supersolutions method in \(H^{\alpha ,\beta ; \psi }_{p}(\Omega )\). Rend Circ Mat Palermo II Ser 2:1–13

• Sousa JVDC, Capelas de Oliveira E (2018) On the \(\psi \)-Hilfer fractional derivative. Commun Nonlinear Sci Numer Simul 60:72–91

  Article  MathSciNet  Google Scholar 

• Sousa JVDC, Ledesma CT, Pigossi M, Zuo J (2022a) Nehari manifold for weighted singular fractional \(p\)-Laplace equations. Bull Braz Math Soc 53(4):1245–1275

  Article  MathSciNet  Google Scholar 

• Sousa JVDC, Zuo J, O’Regan D (2022b) The Nehari manifold for a \(\psi \)-Hilfer fractional \(p\)-Laplacian. Appl Anal 101(14):5076–5106

  Article  MathSciNet  Google Scholar 

• Sousa J, Lima KB, Tavares LS (2023a) Existence of solutions for a singular double phase problem involving a \(\psi \)-Hilfer fractional operator via Nehari manifold. Qual Theory Dyn Syst 22(3):1–26

  Article  MathSciNet  Google Scholar 

• Sousa JVDC, Lamine M, Tavares LS (2023b) Generalized telegraph equation with fractional \(m(\xi )\)-Laplacian. Minimax Theory Appl 08(2):423–441

  MathSciNet  Google Scholar 

• Sousa JVDC, Kucche KD, Nieto JJ (2024) Existence and multiplicity of solutions for fractional \(\kappa (\xi )\)-Kirchhoff-type equation. Qual Theory Dyn Sys 23(1):27

  Article  MathSciNet  Google Scholar 

• Srivastava HM, Nain AK, Vats RK, Das P (2023) A theoretical study of the fractional-order \(p\)-Laplacian nonlinear Hadamard type turbulent flow models having the Ulam-Hyers stability. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 117(4):160

  Article  MathSciNet  Google Scholar 

• Straughan B (2018) Bidispersive double diffusive convection. Int J Heat Mass Transf 126:504–508

  Article  Google Scholar 

• Sun X, Song Y, Liang S, Zhang B (2023) Critical Kirchhoff equations involving the \(p\)-sub-Laplacians operators on the Heisenberg group. Bull Math Sci 13(02):2250006

  Article  MathSciNet  Google Scholar 

• Tian J, Zhang B (2024) A fractional profile decomposition and its application to Kirchhoff-type fractional problems with prescribed mass. Adv Nonlinear Anal 13(1):20240029

  Article  MathSciNet  Google Scholar 

• Vázquez JL (2006) Smoothing and decay estimates for nonlinear diffusion equations: equations of porous medium type, vol 33. OUP, Oxford

  Book  Google Scholar 

• Vetro C (2022) Variable exponent \(p(x)\)-Kirchhoff type problem with convection. J Math Anal Appl 506(2):125721

  Article  MathSciNet  Google Scholar 

• Wang T, Yang Y, Guo H (2023) Nodal solutions with a prescribed number of nodes for the Kirchhoff-type problem with an asymptotically cubic term. Adv Nonlinear Anal 12(1):20220323

  Article  MathSciNet  Google Scholar 

• Xiang M, Zhang B, Guo X (2015) Infinitely many solutions for a fractional Kirchhoff type problem via fountain theorem. Nonlinear Anal Theory Methods Appl 120:299–313

  Article  MathSciNet  Google Scholar 

• Zhang J (2022) Existence results for a Kirchhoff-type equations involving the fractional \(p_{1}(x), p_{2}(x)\)-Laplace operator. Collectanea Math 2022:1–23

  Google Scholar 

• Zhao M, Song Y, Repovš DD (2024) On the \(p\)-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy–Littlewood–Sobolev nonlinearity. Demonstratio Math 57(1):20230124

  Article  Google Scholar 

• Zuo J, An T, Fiscella A (2021) A critical Kirchhoff?type problem driven by a \(p(\cdot )\)-fractional Laplace operator with variable \(s(\cdot )\)-order. Math Methods Appl Sci 44(1):1071–1085

  Article  MathSciNet  Google Scholar 

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