A \(p(x)\)-Kirchhoff type problem involving the \(p(x)\)-Laplacian-like operators with Dirichlet boundary condition
Abstract
Keywords
Full Text:
PDFReferences
Abbassi, A., Allalou, C., Kassidi, A., Existence of weak solutions for nonlinear $p$-elliptic problem by topological degree, Nonlinear Dyn. Syst. Theory, textbf{20}(2020), no. 3, 229-241.
Abbassi, A., Allalou, C., Kassidi, A., Existence results for some nonlinear elliptic equations via topological degree methods, J. Elliptic Parabol Equ., textbf{7}(2021), no. 1, 121-136.
Acerbi, E., Mingione, G., Regularity results for stationary electro-rheological fluids, Archive for Rational Mechanics and Analysis, textbf{164}(2002), no. 3, 213-259.
Acerbi, E., Mingione, G., {Gradient estimates for the $p(x)$-Laplacean system, Journal f"{u}r die Reine und Angewandte Mathematik, textbf{584}(2005), 117-148.
Afrouzi, G.A., Kirane, M., Shokooh, S., Infinitely many weak solutions for $p(x)$-Laplacian-like problems with Neumann condition, Complex Var. Elliptic Equ., textbf{63}(2018), no. 1, 23-36.
Berkovits, J., Extension of the Leray-Schauder degree for abstract Hammerstein type mappings, J. Differ. Equ., textbf{234}(2007), 289-310.
Chu, C.M., Xiao, Y.X., The multiplicity of nontrivial solutions for a new $p(x)-$Kirchhoff-Type elliptic problem, J. Funct. Spaces, textbf{2021}(2021), 1569376.
Corsato, C., De Coster, C., Obersnel, F., Omari, P., Qualitative analysis of a curvature equation modeling MEMS with vertical load,
Nonlinear Anal. Real World. Appl., textbf{55}(2020), 103-123.
Corsato, C., De Coster, C., Omari, P., The Dirichlet problem for a prescribed anisotropic mean curvature equation: Existence,
uniqueness and regularity of solutions, J. Differential Equations, textbf{260}(2016), no. 5, 4572-4618.
Dai, G., Hao, R., Existence of solutions for a $p(x)$-Kirchhoff-type equation, J. Math. Anal. Appl., textbf{359}(2009), 275-284.
Etemad, S., Matar, M.M., Ragusa, M.A., Rezapour, S.,
Tripled fixed points and existence study to a tripled impulsive fractional differential system via measures of noncompactness,
Mathematics, textbf{10}(2022), no. 1, 25.
Fan, X.L., Zhao, D., On the spaces $L^{p(x)}(Omega)$ and $W^{m,p(x)}(Omega)$, J. Math. Anal. Appl., textbf{263}(2001), 424-446.
Finn, R., Equilibrium Capillary Surfaces, Grundlehren der Mathematischen Wis-senschaften, Springer-Verlag, New York, textbf{284}(1986).
Giusti, E., Minimal Surfaces and Functions of Bounded Variation,
Monographs in Mathematics, Birkh"auser Verlag, Basel, textbf{80}(1984).
Goodrich, C.S., Ragusa, M.A., Scapellato, A., Partial regularity of solutions to $p(x)-$Laplacian PDEs with discontinuous coefficients,
Journal of Differential Equations, textbf{268}(2020), no. 9, 5440-5468.
Kim, I.S., Hong, S.J., A topological degree for operators of generalized $(S_{+})$ type, Fixed Point Theory and Appl., textbf{1}(2015), 1-16.
Kirchhoff, G., Mechanik, Teubner, Leipzig, 1883.
Kov'{a}v{c}ik, O., R'{a}kosn'{i}k, J., On spaces $L^{p(x)}$ and $W^{1,p(x)}$, Czechoslovak Math. J., textbf{41}(1991), no. 4, 592-618.
Lapa, E.C., Rivera, V.P., Broncano, J.Q.,
No-flux boundary problems involving $p(x)$-Laplacian-like operators,
Electron. J. Diff. Equ, {bf 219}(2015), 1-10.
Ni, W.M., Serrin, J., Non-existence theorems for quasilinear partial differential equations,
Rend. Circ. Mat. Palermo (2) Suppl., textbf{8}(1985), 171-185.
Ni, W.M., Serrin, J., Existence and non-existence theorems for ground states for quasilinear partial differential equations,
Att. Conveg. Lincei, textbf{77}(1986), 231-257.
Ouaarabi, M.E., Abbassi, A., Allalou, C., Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation
in weighted Sobolev spaces, J. Elliptic Parabol Equ., textbf{7}(2021), no. 1, 221-242.
Ouaarabi, M.E., Abbassi, A., Allalou, C., Existence result for a general nonlinear degenerate elliptic problems with measure datum in weighted Sobolev spaces, International Journal on Optimization and Applications, textbf{1}(2021), no. 2, 1-9.
Ouaarabi, M.E., Abbassi, A., Allalou, C., Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear
degenerate elliptic problems with measure data, International Journal of Nonlinear Analysis and Applications, textbf{13}(2021), no. 1, 2635-2653.
Ouaarabi, M.E., Allalou, C., Abbassi, A., On the Dirichlet problem for some nonlinear degenerated elliptic equations with weight,
$7^{mbox{th}}$ International Conference on Optimization and Applications (ICOA), 2021, 1-6.
Ru{a}dulescu, V.D., Repovev{s}, D.D., Partial Differential Equations with Variable Exponents, Variational Methods and Qualitative Analysis, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, 2015.
Ragusa, M.A., Razani, A., Safari, F., Existence of radial solutions for a $p(x)$-Laplacian Dirichlet problem, Advances in Difference Equations, textbf{2021}(2021), no. 1, 1-14.
Ragusa M.A., Tachikawa A., On continuity of minimizers for certain quadratic growth functionals, Journal of the Mathematical Society of Japan, textbf{57}(2005), no. 3, 691-700.
Ragusa M.A., Tachikawa A., Regularity of minimizers of some variational integrals with discontinuity, Zeitschrift f"{u}r Analysis und ihre Anwendungen, textbf{27}(2008), no. 4, 469-482.
Rajagopal, K.R., R.uzicka, M., Mathematical modeling of electrorheological materials, Continuum Mechanics and Thermodynamics, textbf{13}(2001), no. 1, 59-78.
Rodrigues, M.M., Multiplicity of solutions on a nonlinear eigenvalue problem for $p(x)$-Laplacian-like operators, Mediterr. J. Math., textbf{9}(2012), 211-223.
R.uzicka, M., Electrorheological Fuids: Modeling and Mathematical Theory, Springer Science & Business Media, 2000.
Zeidler, E., Nonlinear Functional Analysis and its Applications II/B,
Springer-Verlag, New York, 1990.
Zhikov, V.V.E., Averaging of functionals of the calculus of variations and elasticity theory,
Mathematics of the USSR-Izvestiya, textbf{29}(1987), no. 1, 33-66.
DOI: http://dx.doi.org/10.24193/subbmath.2024.2.07
Refbacks
- There are currently no refbacks.