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Multiple solutions for a Navier boundary value problem involving the $p$--biharmonic operator

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  • The existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$--biharmonic operator is investigated. Our approach is chiefly based on critical point theory.
    Mathematics Subject Classification: Primary: 35J40, 35J60.


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  • [1]

    G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 343 (2008), 1166-1176.doi: 10.1016/j.jmaa.2008.01.049.


    G. Bonanno and B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-3640.doi: 10.1016/j.amc.2010.10.019.


    G. Bonanno and B. Di Bella, Infinitely many solutions for a fourth-order elastic beam equation, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 357-368.doi: 10.1007/s00030-011-0099-0.


    G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059.doi: 10.1016/j.jde.2008.02.025.


    G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1-10.doi: 10.1080/00036810903397438.


    H. M. Guo and D. Geng, Infinitely many solutions for the Dirichlet problem involving the $p$-biharmonic-like equation, J. South China Normal Univ. Natur. Sci. Ed., 2009, 18-21, 28.


    M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18 (2005), 439-444.


    G. Han and Z. Xu, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear Anal., 68 (2008), 3646-3656.doi: 10.1016/j.na.2007.04.007.


    C. Li and C.-L. Tang, Three solutions for a Navier boundary value problem involving the $p$-biharmonic, Nonlinear Anal., 72 (2010), 1339-1347.doi: 10.1016/j.na.2009.08.011.


    X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary value problems with parameters, J. Math. Anal. Appl., 327 (2007), 362-375.doi: 10.1016/j.jmaa.2006.04.021.


    A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal., 31 (1998), 895-908.doi: 10.1016/S0362-546X(97)00446-X.


    B. Ricceri, A general variational principle and some of its applications. Fixed point theory with applications in nonlinear analysis, J. Comput. Appl. Math., 133 (2000), 401-410.doi: 10.1016/S0377-0427(99)00269-1.


    G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 3 (1976), 697-718.


    Y. Wang and Y. Shen, Infinitely many sign-changing solutions for a class of biharmonic equation without symmetry, Nonlinear Anal., 71 (2009), 967-977.doi: 10.1016/j.na.2008.11.052.


    W. Wang and P. Zhao, Nonuniformly nonlinear elliptic equations of $p$-biharmonic type, J. Math. Anal. Appl., 348 (2008), 730-738.doi: 10.1016/j.jmaa.2008.07.068.


    Z. Yang, D. Geng and H. Yan, Existence of nontrivial solutions in $p$-biharmonic problems with critical growth, (Chinese) Chinese Ann. Math. Ser. A, 27 (2006), 129-142.

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