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Solutions for a nonhomogeneous p&q-Laplacian problem via variational methods and sub-supersolution technique

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper it is obtained, through variational methods and sub-supersolution arguments, existence and multiplicity of solutions for a nonhomogeneous problem which arise in several branches of science such as chemical reactions, biophysics and plasma physics. Under a general hypothesis it is proved an existence result and multiple solutions are obtained by considering an additional natural condition.
Rocznik
Strony
603--613
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Universidade Federal do Cariri, Centro de Ciências e Tecnologia, Juazeiro do Norte/CE, Brazil
  • Universidade Federal do ABC, Centro de Matemática, Computação e Cognição, Santo André/SP, Brazil
Bibliografia
  • [1] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349–381.
  • [2] V. Ambrosio, Fractional (p, q)-Schrödinger equations with critical and supercritical growth, Appl. Math. Optim. 86 (2022), Article no. 31.
  • [3] V. Ambrosio, T. Isernia, Multiplicity of positive solutions for a fractional p&q-Laplacian problem in RN, J. Math. Anal. Appl. 501 (2021), 31 pp.
  • [4] V. Ambrosio, T. Isernia, A multiplicity result for a (p, q)-Schrödinger–Kirchhoff type equation, Ann. Mat. Pura Appl. 201 (2022), 943–984.
  • [5] V. Ambrosio, V. Rˇadulescu, Fractional double-phase patterns: concentration and multiplicity of solutions, J. Math. Pures Appl. 9 (2020), 101–145.
  • [6] V. Ambrosio, D. Repovš, Multiplicity and concentration results for a (p, q)-Laplacian problem in RN, Z. Angew. Math. Phys. 72 (2021), 33 pp.
  • [7] S.C.Q. Arruda, R.G. Nascimento, Existence and multiplicity of positive solutions for singular p&q-Laplacian problems via sub-supersolution method, Electron. J. Differential Equations 2021 (2021), 11 pp.
  • [8] S.C.Q. Arruda, R.G. Nascimento, Existence and multiplicity of positive solutions for a singular system via sub-supersolution method and mountain pass theorem, Electron. J. Qual. Theory Differ. Equ. 2021 (2021), 20 pp.
  • [9] L. Cherfils, Y. Ilyasov, On the stationary solutions of generalized reaction diffusion equations with p&q-Laplacian, Commun. Pure Appl. Anal. 4 (2005), 9–22.
  • [10] F.J.S.A. Corrêa, A.S.S. Corrêa, G.M. Figueiredo, Existence of positive solution for a singular system involving general quasilinear operators, Differ. Equ. Appl. 6 (2014), 481–494.
  • [11] F.J.S.A. Corrêa, A.S.S. Corrêa, G.M. Figueiredo, Positive solution for a class of p&q-singular elliptic equation, Nonlinear Anal. Real World Appl. 16 (2014), 163–169.
  • [12] G.M. Figueiredo, Existence of positive solutions for a class of p&q elliptic problems with critical growth on RN, J. Math. Anal. Appl. 378 (2011), 507–518.
  • [13] Y.T. Guo, G.J. Ye, Existence and uniqueness of weak solutions to variable-order fractional Laplacian equations with variable exponents, J. Funct. Spaces 2021 (2021), Article ID 6686213.
  • [14] C. He, G. Li, The regularity of weak solutions to nonlinear scalar field elliptic equations containing p&q-Laplacians, Ann. Acad. Sci. Fenn. Math. 33 (2008), 337–371.
  • [15] T. Isernia, D. Repovš, Nodal solutions for double phase Kirchhoff problems with vanishing potentials, Asymptot. Anal. 124 (2021), 371–396.
  • [16] M.A. Ragusa, Parabolic Herz spaces and their applications, Appl. Math. Lett. 25 (2012), 1270–1273.
  • [17] K.C.V. de Sousa, L.S. Tavares, Multiple solutions for a class of problems involving the p(x)-Laplacian operator, Appl. Anal. 101 (2021), 5415–5423.
  • [18] G.C.G. dos Santos, G. Figueiredo, J.R.S. Silva, Multiplicity of positive solutions for an anisotropic problem via sub-supersolution method and mountain pass theorem, J. Convex Anal. Analysis 27 (2020), 1363–1374.
  • [19] M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, 2nd ed., Springer, Berlin, 1996.
  • [20] J.B. Zuo, R. Guefaifia, F. Kamache, S. Boulaaras, Multiplicity of solutions for perturbed nonlinear fractional p-Laplacian boundary value systems related with two control parameters, Filomat 35 (2021), 2827–2848.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e094a075-aa17-4777-ab86-9dc6abc96d30
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