Advanced Search
Article Contents
Article Contents

On a functional satisfying a weak Palais-Smale condition

Abstract Related Papers Cited by
  • In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition. An existence result is proved under general assumptions on the nonlinearities.
    Mathematics Subject Classification: Primary: 35j62; Secondary: 46E30, 46E35.


    \begin{equation} \\ \end{equation}
  • [1]

    R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, Vol. 65. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975.


    A. Azzollini, P. d'Avenia and A. Pomponio, Quasilinear elliptic equations in $\mathbbR^N$ via variational methods and Orlicz-Sobolev embeddings, Calc. Var. (to appear). doi: 10.1007/s00526-012-0578-0.


    A. Azzollini and A. Pomponio, On the Schrödinger equation in $\mathbbR^N$ under the effect of a general nonlinear term, Indiana Univ. Math. Journal, 58 (2009), 1361-1378.doi: 10.1512/iumj.2009.58.3576.


    M. Badiale, L. Pisani and S. Rolando, Sum of weighted Lebesgue spaces and nonlinear elliptic equations, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 369-405.doi: 10.1007/s00030-011-0100-y.


    P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorem and applications to some nonlinear problems with "strong'' resonance at infinity, Nonlin. Anal. TMA, 7 (1983), 981-1012.doi: 10.1016/0362-546X(83)90115-3.


    H. Berestycki and P. L. Lions, Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.doi: 10.1007/BF00250555.


    H. Berestycki and P. L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., 82 (1983), 347-375.doi: 10.1007/BF00250556.


    G. Cerami, Un criterio di esistenza per i punti critici su varietà illimitate, Rc. Ist. lomb. Sci. Lett., 112 (1978), 332-336.


    T. D'Aprile and G. Siciliano, Magnetostatic solutions for a semilinear perturbation of the Maxwell equations, Adv. Differential Equations, 16 (2011), 435-466.


    J. Hirata, N. Ikoma and K. Tanaka, Nonlinear scalar field equations in $\mathbbR^N$: Mountain pass and symmetric mountain pass approaches, TMNA, 35 (2010), 253-276.


    L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer-type problem set on $\mathbbR^N$, Proc. R. Soc. Edinb., Sect. A, Math., 129 (1999), 787-809.doi: 10.1017/S0308210500013147.


    E. H. Lieb and M. Loss, Analysis, Second edition. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI, 2001.


    M. Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv., 60 (1985), 558-581.doi: 10.1007/BF02567432.

  • 加载中

Article Metrics

HTML views() PDF downloads(427) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint