Multiple solutions for a class of degenerate nonlocal problems involving sublinear nonlinearities

In this article, we use the three critical points theorem by G. Bonanno [3] in order to investigate the multiplicity of solutions for some nonlocal degenerate problems.

[1]  Guowei Dai,et al.  Existence of solutions for a p(x)-Kirchhoff-type equation , 2009 .

[2]  Kanishka Perera,et al.  Nontrivial solutions of Kirchhoff-type problems via the Yang index , 2006 .

[3]  Chun-Lei Tang,et al.  Existence and multiplicity of solutions for Kirchhoff type equations , 2011 .

[4]  Kanishka Perera,et al.  Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow , 2006 .

[5]  Gabriele Bonanno,et al.  Some remarks on a three critical points theorem , 2003 .

[6]  Benjin Xuan.  The Eigenvalue Problem of a Singular Quasilinear Elliptic Equation , 2003 .

[7]  Xianling Fan,et al.  On nonlocal p(x)-Laplacian Dirichlet problems☆ , 2010 .

[8]  N. T. Chung.  Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities , 2012 .

[9]  Biagio Ricceri,et al.  On an elliptic Kirchhoff-type problem depending on two parameters , 2008, J. Glob. Optim..

[10]  P. Rabinowitz,et al.  Dual variational methods in critical point theory and applications , 1973 .

[11]  Giovany M. Figueiredo,et al.  On an elliptic equation of p-Kirchhoff type via variational methods , 2006, Bulletin of the Australian Mathematical Society.

[12]  Florin Catrina,et al.  On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions † , 2001 .

[13]  Ahmed Bensedik,et al.  On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity , 2009, Math. Comput. Model..

[14]  To Fu Ma,et al.  Remarks on an elliptic equation of Kirchhoff type , 2005 .

[15]  H. Q. Toan,et al.  ON A CLASS OF DEGENERATE NONLOCAL PROBLEMS WITH SIGN-CHANGING NONLINEARITIES , 2012 .

[16]  Robert V. Kohn,et al.  First order interpolation inequalities with weights , 1984 .

[17]  L. Kong,et al.  A Variational Approach to a Kirchhoff-type Problem Involving Two Parameters , 2013 .

[18]  Duchao Liu.  On a p-Kirchhoff equation via Fountain Theorem and Dual Fountain Theorem☆ , 2010 .

[19]  Giovany M. Figueiredo,et al.  On a p-Kirchhoff equation via Krasnoselskii's genus , 2009, Appl. Math. Lett..