Infinitely many solutions for a nonlinear Navier problem involving the p-biharmonic operator

• Autores: Filippo Cammaroto
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 501-519
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0501
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo establecemos algunos resultados sobre la existencia de infinitas soluciones para una ecuación elíptica que involucra los operadores p-biarmónico y p-Laplaciano acoplados con condiciones de borde de Navier, donde las nolinealidades dependen de dos parámetros reales y no satisfacen ninguna condición simétrica. La naturaleza del enfoque es variacional y la herramienta principal es un resultado abstracto de Ricceri. La novedad de la aplicación de esta herramienta abstracta es el uso de una clase de funciones test que hacen que las hipótesis sobre la data sean más fáciles de verificar.

  • English

    Abstract In this paper we establish some results of existence of infinitely many solutions for an elliptic equation involving the p-biharmonic and the p-Laplacian operators coupled with Navier boundary conditions where the nonlinearities depend on two real parameters and do not satisfy any symmetric condition. The nature of the approach is variational and the main tool is an abstract result of Ricceri. The novelty in the application of this abstract tool is the use of a class of test functions which makes the assumptions on the data easier to verify.

• Referencias bibliográficas
  • Afrouzi, G. A.,Shokooh, S.. (2015). Existence of infinitely many solutions for quasilinear problems with a p(x)-biharmonic operator. Electron....
  • Arioli, G.,Gazzola, F.,Grunau, H. C.. (2006). Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity....
  • Bai, C.. (2013). Infinitely many solutions for a perturbed nonlinear fractional boundary-value problem. Electron. J. Differ. Equations. 12
  • Ben Ayed, M.,Selmi, A.. (2009). Concentration phenomena for a fourth-order equation on ℝn. Pacific J. Math.. 242. 1-32
  • Bueno, H.,Paes-Leme, L.,Rodrigues, H.. (2018). Multiplicity of solutions for p-biharmonic problems with critical growth. Rocky Mountain J....
  • Cammaroto, F.. (2020). Sequences of weak solutions to a fourth-order elliptic problem. Atti Accad. Peloritana Pericolanti Cl. di Sci. Fis....
  • Cammaroto, F.,Chinnì, A.,Di Bella, B.. (2005). Infinitely many solutions for the Dirichlet problem involving the p-Laplacian. Nonlinear Anal.....
  • Cammaroto, F.,Vilasi, L.. (2019). Sequences of weak solutions for a Navier problem driven by the p(x)-biharmonic operator. Minimax Theory...
  • Candito, P.,Li, L.,Livrea, R.. (2012). Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the p-biharmonic....
  • Candito, P.,Livrea, R.. (2010). Infinitely many solution for a nonlinear Navier boundary value problem involving the p-biharmonic. Stud. Univ....
  • Carrião, P. C.,Demarque, R.,Miyakagi, O. H.. (2014). Nonlinear biharmonic problems with singular potentials. Commun. Pure Appl. Anal.. 13....
  • Chen, Q.,Chen, C.. (2017). Infinitely many solutions for a class of p-biharmonic equation in ℝn. Bull. Iranian Math. Soc.. 43. 205
  • Cheng, B.,Tang, X.. (2017). High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential. Comput....
  • Dai, G.. (2009). Infinitely many non-negative solutions for a Dirichlet problem involving p(x)-Laplacian. Nonlinear Anal.. 71. 5840
  • Dai, G.,Wei, J.. (2010). Infinitely many non-negative solutions for a p(x)-Kirchhoff-type problem with Dirichlet boundary condition. Nonlinear...
  • Figuereido, G. M.,Nascimento, R. G.. (2016). Multiplicity of solutions for equations involving a nonlocal term and the biharmonic operator....
  • Furusho, Y.,Takaŝi, K.. (1998). Positive entire solutions to nonlinear biharmonic equations in the plane. J. Comput. Appl. Math.. 88. 161
  • Guo, Z.,Wei, J.. (2010). Qualitative properties of entire radial solutions for a biharmonic equation with supercritical nonlinearity. Proc....
  • Guo, Z.,Wei, J.,Yang, W.. (2016). On nonradial singular solutions of supercritical biharmonic equations. Pacific J. Math.. 284. 395-430
  • Hadjian, A.,Ramezani, M.. (2017). Existence of infinitely many solutions for fourth-order equations depending on two parameters. Electron....
  • Heidari Tavani, M. R.,Nazari, A.. (2019). Infinitely many weak solutions for a fourth-order equation with nonlinear boundary conditions. Miskolc...
  • Heidarkhani, S.. (2014). Infinitely many solutions for systems of n fourth order partial differential equations coupled with Navier boundary...
  • Kristály, A.. (2006). Infinitely many solutions for a differential inclusion problem in ℝN. J. Differential Equations. 220. 511
  • Lazer, A. C.,McKenna, P. J.. (1990). Large amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis....
  • Liu, L.,Chen, C.. (2016). Infinitely many solutions for p-biharmonic equation with general potential and concave-convex nonlinearity in ℝN....
  • Liu, C.,Wang, J.. (2013). Existence of multiple solutions for a class of biharmonic equations. Discrete Dyn. Nat. Soc.. 5
  • Makvand Chaharlang, M.,Razani, A.. (2019). Existence of infinitely many solutions for a class of nonlocal problems with Dirichlet boundary...
  • Makvand Chaharlang, M.,Razani, A.. (2018). Infinitely many solutions for a fourth order singular elliptic problem. Filomat. 32. 5003
  • Massar, M.,Hssini, E. M.,Tsouli, N.. (2012). Infinitely many solutions for class of Navier boundary (p, q)-biharmonic systems. Electron. J....
  • McKenna, P. J.,Reichel, W.. (2003). Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry. Electron....
  • McKenna, P. J.,Walter, W.. (1987). Nonlinear oscillations in a suspension bridge. Arch. Rational Mech. Anal.. 98. 167
  • McKenna, P. J.,Walter, W.. (1990). Travelling waves in a suspension bridge. SIAM J. Appl. Math.. 50. 703
  • Miao, Q.. (2019). Multiple solutions for nonlocal elliptic systems involving p(x)-biharmonic operator. Mathematics. 7. 10
  • Ricceri, B.. (2000). A general variational principle and some of its applications. J. Comput. Appl. Math.. 113. 401
  • Shokooh, S.,Afrouzi, G. A.. (2019). Infinitely many solutions for a class of fourth-order impulsive differential equations. Adv. Pure Appl....
  • Shokooh, S.,Afrouzi, G. A.,Zahmatkesh, H.. (2018). Infinitely many weak solutions for fourth-order equations depending on two parameters....
  • Song, Y.. (2014). A nonlinear boundary value problem for fourth-order elastic beam equations. Bound. Value Probl.. 11
  • Sun, F.,Liu, L.,Wu, Y.. (2017). Infinitely many sign-changing solutions for a class of biharmonic equation with p-Laplacian and Neumann boundary...
  • Teng, K.. (2013). Infinitely many solutions for a class of fractional boundary value problems with nonsmooth potential. Abst. Appl. Anal.. 6
  • Wang, Y.,Shen, Y.. (2009). Infinitely many sign-changing solutions for a class of biharmonic equation without symmetry. Nonlinear Anal.. 71....
  • Xu, M.,Bai, C.. (2015). Existence of infinitely many solutions for pertubed Kirchhoff type elliptic problems with Hardy potential. Electron....
  • Zhang, J.. (2011). Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems. Electron. J. Qual....
  • Zhang, J.,Wei, Z.. (2011). Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems. Nonlinear...