Nonresonance below the second eigenvalue for a nonlinear elliptic problem
DOI:
https://doi.org/10.4067/S0716-09172003000100001Keywords:
Eigenvalue, Nonresonance, p-laplacian, Variational approach.Abstract
We study the solvability of the problem ??pu = g(x, u) + h in ?; u = 0 on ??, when the nonlinearity g is assumed to lie asymptotically between 0 and the second eigenvalue ?2 of ??p. We show that this problem is nonresonant.References
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[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).
Published
2017-04-24
How to Cite
[1]
M. Moussaoui and M. Moussaoui, “Nonresonance below the second eigenvalue for a nonlinear elliptic problem”, Proyecciones (Antofagasta, On line), vol. 22, no. 1, pp. 1-13, Apr. 2017.
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