A critical p-biharmonic system with negative exponents

Abstract In this paper, we are devoted to the study of critical p -biharmonic system with a parameter λ , which involves strongly-coupled critical nonlinearities and negative exponents. We prove that there exists a positive constant λ ∗ such that the above problem admits at least two solutions if λ ∈ ( 0 , λ ∗ ) .

[1]  Vicentiu D. Radulescu,et al.  On a p(⋅)-biharmonic problem with no-flux boundary condition , 2016, Comput. Math. Appl..

[2]  E. Jannelli,et al.  Nonlinear critical problems for the biharmonic operator with Hardy potential , 2015 .

[3]  Francisco Bernis,et al.  Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order , 1996, Advances in Differential Equations.

[4]  Jihui Zhang,et al.  Existence of solutions for a class of biharmonic equations with critical nonlinearity in RNRN , 2016 .

[5]  P. Drábek,et al.  Global Bifurcation Result for the p-biharmonic Operator , 2001 .

[6]  Wei Zhang,et al.  Sign-changing solutions for p-biharmonic equations with Hardy potential☆ , 2017 .

[7]  Elliott H. Lieb,et al.  A Relation Between Pointwise Convergence of Functions and Convergence of Functionals , 1983 .

[8]  D. Kang,et al.  Asymptotic behavior and existence results for the biharmonic problems involving Rellich potentials , 2017 .

[9]  Ignacio Guerra A note on nonlinear biharmonic equations with negative exponents , 2012 .

[10]  On the p-biharmonic equation involving concave-convex nonlinearities and sign-changing weight function , 2012 .

[11]  Lin Li,et al.  Existence of three solutions for (p, q)-biharmonic systems , 2010 .

[12]  Yijing Sun,et al.  An exact estimate result for a class of singular equations with critical exponents , 2011 .

[13]  Some existence results of bounded variation solutions to 1-biharmonic problems , 2018, Journal of Mathematical Analysis and Applications.

[14]  Jirí Benedikt Spectra of fourth-order quasilinear problems , 2007, Math. Comput. Simul..

[15]  P. Candito,et al.  Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the p-biharmonic , 2012 .

[16]  N. Ghoussoub,et al.  The Critical Dimension for a Fourth Order Elliptic Problem with Singular Nonlinearity , 2008, 0904.2414.

[17]  Yisong Yang,et al.  Nonlinear non-local elliptic equation modelling electrostatic actuation , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  D. Ye,et al.  Stability for entire radial solutions to the biharmonic equation with negative exponents , 2018, Comptes Rendus Mathematique.

[19]  Claudianor O. Alves,et al.  On systems of elliptic equations involving subcritical or critical Sobolev exponents , 2000 .

[20]  Lingju Kong,et al.  Positive radial solutions for quasilinear biharmonic equations , 2016, Comput. Math. Appl..

[21]  Giovanni Molica Bisci,et al.  Multiple solutions of p-biharmonic equations with Navier boundary conditions , 2014, 1608.07423.

[22]  F. Gazzola,et al.  Existence and nonexistence results for critical growth biharmonic elliptic equations , 2003 .

[23]  Chun-Lei Tang,et al.  Three solutions for a Navier boundary value problem involving the p-biharmonic☆ , 2010 .

[24]  M. Bhakta Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials , 2013, 1311.0356.

[25]  Yajing Zhang Positive solutions of semilinear biharmonic equations with critical Sobolev exponents , 2012 .

[26]  D. Kang,et al.  Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities , 2017 .

[27]  G. Talenti,et al.  Best constant in Sobolev inequality , 1976 .

[28]  T. Gyulov,et al.  On a class of boundary value problems involving the p-biharmonic operator , 2010 .

[29]  Baishun Lai The regularity and stability of solutions to semilinear fourth-order elliptic problems with negative exponents , 2016, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[30]  N. Ghoussoub,et al.  On a Fourth Order Elliptic Problem with a Singular Nonlinearity , 2009 .