Existence of solutions for a p-Laplacian Kirchhoff type problem with nonlinear term of superlinear and subcritical growth
Keywords:
Kirchhoff problem, nonlocal quasilinear problem, variational methods, nonnegative and nonpositive solutions.Abstract
This paper is concerned by the study of the existence of nonnegative and nonpositive solutions for a nonlocal quasilinear Kirchhoff problem by using the Mountain Pass lemma technique.
Mathematics Subject Classification (2010): 35A15, 35B38, 35J62, 35J92.
References
Bensedik, A., Sur quelques probl`emes elliptiques de type de Kirchhoff et dynamique des fluides, Doctoral Dissertation, Universit´e Jean Monnet, Saint-Etienne, 2012.
Brezis, H., Analyse Fonctionnelle: Th´eorie et Applications, Editions Masson, Paris, 1983.
Ke, X.F., Tang, C.L., Existence and multiplicity of solutions to semilinear elliptic equation with nonlinear term of superlinear and subcritical growth, Electron. J. Differential Equations, 88(2018), 1-17.
Mao, A., Zhang, Z., Sign changing and multiple solutions of Kirchhoff type problems without the P.S. condition, Nonlinear Anal., 70(2009), 1275-1287.
Otan, M., Teshma, T., On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad. Ser. A Math. Sci., 64(1988), 8-10.
Quoirin, H.R., Lack of coercivity in a concave-convex type equation, Calc. Var. Partial Differential Equations, 37(2010), 523-546.
Struwe, M., Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer, Berlin, 2000.
Willem, M., Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications, vol. 24, Birkha¨user, Boston, 1996.
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