Nonresonance below the second eigenvalue for a nonlinear elliptic problem

• Moussaoui, M. ^[1]
  1. [1] University Mohamed I.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 22, Nº. 1, 2003, págs. 1-13
• Idioma: inglés
• DOI: 10.4067/S0716-09172003000100001
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• Resumen

  • We study the solvability of the problem −∆pu = g(x, u) + h in Ω; u = 0 on ∂Ω, when the nonlinearity g is assumed to lie asymptotically between 0 and the second eigenvalue λ2 of −∆p. We show that this problem is nonresonant.

• Referencias bibliográficas
  • Citas [1] R. A. ADAMS Sobolev spaces, Academic Press, New York, (1975)
  • [2] A. ANANE Simplicité et isolation de la première valeur propre du p-laplacien avec poids C. R. Ac. Sc. Paris, 305 (1987), 725 − 728.
  • [3] A. Anane, O. Chakrone Sur un théorème de point critique et application à un problème de non résonance entre deux valeurs propres du p-laplacien....
  • [4] A. ANANE, N. TSOULI On the second eigenvalue of the p-laplacian, Nonlinear Partial Differential Equations, Pitman Research Notes 343,1-9...
  • [5] BARTOLO. P, BENCI. D. FORTUNATO Abstract critical point theorems and applications to some nonlinear problems with strong resonance at...
  • [6] D. G. COSTA, A. S. OLIVEIRA Existence of solution for a class of semilinear elliptic problems at double resonance Bol. Soc. BRAS. Mat.,...
  • [7] D. G. COSTA, C. A. MAGALHAES Variational elliptic problems which are nonquadratic at infinity. Nonlinear Analysis, vol 23. No 11. 1401-1412...
  • [8] D.G. DE FIGUEIREDO, J.P. GOSSEZ Strict monotonicity of eigenvalues and unique continuation, Comm. Part. Diff. Eq., 17, 339- 346 (1992)
  • [9] M. MOUSSAOUI, A.R. EL AMROUSS Minimax principles for critical- point theory in application to quasilinear boundary-value problems E.J.D.E...
  • [10] M. MOUSSAOUI, M. MOUSSAOUI Nonlinear elliptic problems with resonance at the two first eigenvalue: A variational approach , preprint...
  • [11] M. MOUSSAOUI, M. MOUSSAOUI Nonresonance between nonconsecutive eigenvalues of semilinear elliptic equations: Variational methods, preprint...
  • [12] JOAO. MARCOS. B. do O Solution to perturbed eigenvalue problems of the p-laplacian in RN∗ J. D. E. N 11, 1-15 (1997).
  • [13] P. H. RABINOWITZ minimax methods in critical point theory with application to differential equations, CBMS, Regional conf. Ser. Math.,...
  • [14] E. A. B. SILVA Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA, 16, 455-477 (1991).