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Research Article Open access CC BY 3.0

Three Solutions for a Navier Boundary Value System Involving the (p(x); q(x))-Biharmonic Operator

Honghui Yin, Zuodong Yang

Journal of Advances in Mathematics and Computer Science · pp. 281–290 · Published 29 Apr 2013

10.9734/BJMCS/2013/3166

Abstract

The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the (p(x); q(x))-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [12].

(p(x); q(x))-biharmonic Sobolev space three critical points theorem

References (6)

  1. 1 Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone Operators
  2. 2 Singular solutions of the p-Laplace equation [DOI]
  3. 3 Interpolation inequalities for derivatives in variable exponent Lebesgue–Sobolev spaces [DOI]
  4. 4 Existence and multiplicity of solutions for a Neumann problem involving the -Laplace operator [DOI]
  5. 5 A minimax inequality and its applications to ordinary differential equations [DOI]
  6. 6 On the existence of solutions to a fourth‐order quasilinear resonant problem [DOI]

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Multiple Solutions for Nonlinear Navier Boundary Systems Involving (p1(x), …, pn(x))‐Biharmonic Problem

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