[1] Ahn J H, Kim I H, Kim Y H, Zeng S. Existence results and $L^{\infty}$-bound of solutions to Kirchhoff-Schrödinger-Hardy type equations involving double phase operators. Results Math, 2024, 79: 1-48
[2] Alves C O, Liu S B. On superlinear $p(x)$-Laplacian equations in $\mathbb{R}^N$. Nonlinear Anal, 2010, 73: 2566-2579
[3] Ambrosetti A, Rabinowitz P. Dual variational methods in critical point theory and applications. J Funct Anal, 1973, 14: 349-381
[4] Bahrouni A, Rădulescu V D, Repovš D D. Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves. Nonlinearity, 2019, 32: 2481-2495
[5] Baroni P, Colombo M, Mingione G. Regularity for general functionals with double phase. Calc Var Partial Differential Equations, 2018, 57: 1-43
[6] Bonanno G, Marano S. On the structure of the critical set of non-differentiable functions with a weak compactness condition. Appl Anal, 2010, 89: 1-10
[7] Brezis H. Functional Analysis, Sobolev Spaces and Partial Differential Equation. New York: Springer, 2011
[8] Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc, 1983, 88: 486-490
[9] Cen J, Kim S J, Kim Y H, Zeng S. Multiplicity results of solutions to the double phase anisotropic variational problems involving variable exponent. Adv Differential Equations, 2023, 28: 467-504
[10] Cen J, Vetro C, Zeng S. A multiplicity theorem for double phase degenerate Kirchhoff problems. Appl Math Lett, 2023, 146: 1-6
[11] Choudhuri D. Existence and Hölder regularity of infinitely many solutions to a $p$ Kirchhoff type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition. Z Angew Math Phys, 2021, 72: 1-36
[12] Colasuonno F, Squassina M.Eigenvalues for double phase variational integrals. Ann Mat Pura Appl, 2016, 195: 1917-1959
[13] Colombo M, Mingione G. Regularity for double phase variational problems. Arch Ration Mech Anal, 2015, 215: 443-496
[14] Crespo-Blanco Á, Gasiński L, Harjulehto P, Winkert P. A new class of double phase variable exponent problems: Existence and uniqueness. J Differential Equations, 2022, 323: 182-228
[15] Díaz J I. Nonlinear Partial Differential Equations and Free Boundaries. Vol 1: Elliptic Equations. Boston-London-Melbourne: Pitman Advanced Publishing Program, 1985
[16] Drábek P, Kufner A, Nicolosi F. Quasilinear Elliptic Equations with Degenerations and Singularities. Berlin: De Gruyter, 1997
[17] Drábek P. Nonlinear eigenvalue problem for $p$-Laplacian in $\mathbb{R}^N$. Math Nachr, 1995, 173: 131-139
[18] Fabian M, Habala P, Hajék P, et al. Banach Space Theory: The Basis for Linear and Nonlinear Analysis. New York: Springer, 2011
[19] Ferrara M, Bisci G M. Existence results for elliptic problems with Hardy potential. Bull Sci Math, 2014, 138: 846-859
[20] Fiscella A. A double phase problem involving Hardy potentials. Appl Math Optim, 2022, 85: 1-16
[21] Fiscella A, Pinamonti A. Existence and multiplicity results for Kirchhoff-type problems on a double-phase setting. Mediterr J Math, 2023, 20: 1-19
[22] Fiscella A, Pucci P. Kirchhoff-Hardy fractional problems with lack of compactness. Adv Nonlinear Stud, 2017, 17: 429-456
[23] Garcia Azozero J P, Peral Alonso I. Hardy inequalities and some critical elliptic and parabolic problems. J Differential Equations, 1998, 144: 441-476
[24] Harjulehto P, Hästö P. Orlicz Spaces and Generalized Orlicz Spaces. Cham: Springer, 2019
[25] Heinz H P. Free Ljusternik-Schnirelman theory and the bifurcation diagrams of certain singular nonlinear problems. J Differential Equations, 1987, 66: 263-300
[26] Ho K, Winkert P. Infinitely many solutions to Kirchhoff double phase problems with variable exponents. Appl Math Lett, 2023, 145: 1-8
[27] Hurtado E J, Miyagaki O H, Rodrigues R S. Existence and multiplicity of solutions for a class of elliptic equations without Ambrosetti-Rabinowitz type conditions. J Dynam Differential Equations, 2018, 30: 405-432
[28] Joe W J, Kim S J, Kim Y H, Oh M W. Multiplicity of solutions for double phase equations with concave-convex nonlinearities. J Appl Anal Comput, 2021, 11: 2921-2946
[29] Khodabakhshi M, Aminpour A M, Afrouzi G A, Hadjian A. Existence of two weak solutions for some singular elliptic problems. Rev R Acad Cienc Exactas Fís Nat Ser A Math RACSAM, 2016, 110: 385-393 % https://doi.org/10.1007/s13398-015-0239-1
[30] Khodabakhshi M, Hadjian A. Existence of three weak solutions for some singular elliptic problems. Complex Var Elliptic Equ, 2018, 63: 68-75
[31] Kim Y H, Ahn J H, Lee J, Zeng S. Multiplicity and a-priori bounds of solutions to Kirchhoff-Schrödinger-Hardy type equations involving the $p$-Laplacian. submitted. Kim Y H, Jeong T J. Multiplicity results of solutions to the double phase problems of Schrödinger-Kirchhoff type with concave-convex nonlinearities. Mathematics, 2024, 12: 1-35
[32] Kirchhoff G R.Vorlesungen über Mathematische Physik. Leipzig: Teubner, 1876
[33] Lee J I, Kim Y H. Multiplicity of radially symmetric small energy solutions for quasilinear elliptic equations involving nonhomogeneous operators. Mathematics, 2020, 8: 1-15
[34] Lin X, Tang X H. Existence of infinitely many solutions for $p$-Laplacian equations in $\Bbb R^{N}$. Nonlinear Anal, 2013, 92: 72-81
[35] Liu W, Dai G. Existence and multiplicity results for double phase problem. J Differential Equations, 2018, 265: 4311-4334
[36] Nachman A, Callegari A. A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM J Appl Math, 1980, 38: 275-281
[37] Piersanti P, Pucci P. Entire solutions for critical $p$-fractional Hardy Schrödinger Kirchhoff equations. Publ Mat, 2018, 62: 3-36
[38] Pucci P, Xiang M, Zhang B. Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional $p$-Laplacian in $\mathbb{R}^N$. Calc Var Partial Differential Equations, 2015, 54: 2785-2806
[39] Ricceri B. A further three critical points theorem. Nonlinear Anal, 2009, 71: 4151-4157
[40] Ricceri B. Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions. Adv Nonlinear Anal, 2024, 13: 1-7
[41] Simon J.Régularité de la solution dune équation non linéaire dans $\mathbb{R}^N$//Bénilan P, Robert J. Journees d'Analyse Non Lineaire. Berlin: Springer, 1978
[42] Tan Z, Fang F. On superlinear $p(x)$-Laplacian problems without Ambrosetti and Rabinowitz condition. Nonlinear Anal, 2012, 75: 3902-3915
[43] Vergara V, Zacher R. A priori bounds for degenerate and singular evolutionary partial integro-differential equations. Nonlinear Anal, 2010, 73: 3572-3585
[44] Wang Z Q. Nonlinear boundary value problems with concave nonlinearities near the origin. NoDEA Nonlinear Differential Equations Appl, 2001, 8: 15-33
[45] Willem M. Minimax Theorems. Basel: Birkhauser, 1996
[46] Zhao M, Song Y, Repovš, D D. On the $p$-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity. Demonstr Math, 2024, 57: 1-18
[47] Zhikov V V. Averaging of functionals of the calculus of variations and elasticity theory. Mathematics of the USSR-Izvestiya, 1986, 50: 675-710
[48] Zhikov V V. On Lavrentiev's phenomenon. Russ J Math Phys, 1995, 3: 249-269
