Nonresonance below the second eigenvalue for a nonlinear elliptic problem

  • M. Moussaoui University Mohamed I.
  • M. Moussaoui University Mohamed I.
Palabras clave: Eigenvalue, Nonresonance, p-laplacian, Variational approach.

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.

Biografía del autor

M. Moussaoui, University Mohamed I.
Department of Mathematics, Faculty of Sciences.
M. Moussaoui, University Mohamed I.
Department of Mathematics, Faculty of Sciences.

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. Annales de la Faculté des Sciences de Toulouse, Vol IX,No 1, 2000, p.5-30.

[4] A. ANANE, N. TSOULI On the second eigenvalue of the p-laplacian, Nonlinear Partial Differential Equations, Pitman Research Notes 343,1-9 (1996)

[5] BARTOLO. P, BENCI. D. FORTUNATO Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Analysis 7, 981-1012 (1983).

[6] D. G. COSTA, A. S. OLIVEIRA Existence of solution for a class of semilinear elliptic problems at double resonance Bol. Soc. BRAS. Mat., vol 19, (1988) 21-37.

[7] D. G. COSTA, C. A. MAGALHAES Variational elliptic problems which are nonquadratic at infinity. Nonlinear Analysis, vol 23. No 11. 1401-1412 (1994).

[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 vol (2000) N 18 p 1-9.

[10] M. MOUSSAOUI, M. MOUSSAOUI Nonlinear elliptic problems with resonance at the two first eigenvalue: A variational approach , preprint (2000).

[11] M. MOUSSAOUI, M. MOUSSAOUI Nonresonance between nonconsecutive eigenvalues of semilinear elliptic equations: Variational methods, preprint (2000).

[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., vol 65 AMS, Providence Ri. (1986).

[14] E. A. B. SILVA Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA, 16, 455-477 (1991).
Publicado
2017-04-24
Cómo citar
Moussaoui, M., & Moussaoui, M. (2017). Nonresonance below the second eigenvalue for a nonlinear elliptic problem. Proyecciones. Journal of Mathematics, 22(1), 1-13. https://doi.org/10.4067/S0716-09172003000100001
Sección
Artículos