Solutions for Some Elliptic Problems with Double Resonance

Aixia Qian


In this paper, we prove the existence results and multiplicity results of nontrivial solutions for some elliptic problems with double resonance by using Morse theory.


Double resonance; Critical group; Morse theory; Semilinear elliptic equation

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K.C. Chang, Infinite Dimensional Morse Thoery and Multiple Solutios Problems , Birkhauser, Boston, 1993.

K.C. Chang, Morse theory in nonlinear analysis, Proc. Sympos. ICTP (1997).

T. Bartsch and S.J. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonl. Anal. 28 (1997), 419-441.

S.J. Li and J.Q. Liu, Computations of critical groups at degenerate critical point and applications to nonlinear differential equations with resonace, Houson J. Math. 25 (1999), 563-582.

S.J. Li and M. Willem, Multiple solutions for asymptotically linear boundary value problems in which the nonlineariy cross at least one eigenvalue, Nonl. Diff. Equa. Appl. 5 (1998), 479-490.

S.B. Liu, Critical Groups at Infinite, Multiple Solutions for Nonlinear Elliptic Equations , Doctorial Dissertation, 2003.

R. Molle and D. Passaseo, Nonlinear elliptic equations with large supercritical exponents, Calc. Var. 26 (2006), 201-225.

A.X. Qian, Neumann problem of elliptic equation with strong resonance, Nonl Anal T.M.A. 66 (2007), 1885-1898.

M. Ramos, Remarks on resonance problems with unbounded perturbations, Diff. Intg. Eqns. 6 (1998), 215-223.

J.B. Su, Existence and multiplicity results for classes of elliptic resonant problems, J. Math. Anal. Appl. 273 (2002), 565-579.

Z.T. Zhang and S.J. Li, On sign-changing and multiple solutions of the $p$-laplacian, J. Funt. Anal. 197 (2003), 447-468



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