Artículos de revistas
Multiplicity Results For Some Quasilinear Elliptic Problems
Registro en:
Topological Methods In Nonlinear Analysis. , v. 34, n. 1, p. 77 - 89, 2009.
12303429
2-s2.0-77956458616
Autor
De Paiva F.O.
DoO J.M.
De Medeiros E.S.
Institución
Resumen
In this paper, we study multiplicity of weak solutions for the following class of quasilinear elliptic problems of the form -Δ pu - Δu = g(u) - λ|u| q-2u in Σ with u = 0 on ∂Σ, where Σ is a bounded domain in ℝ n with smooth boundary ∂Σ, 1 < q < 2 < p ≤ n, λ is a real parameter, Δ pu = div(|∇u| p-2∇u) is the p-Laplacian and the nonlinearity g(u) has subcritical growth. The proofs of our results rely on some linking theorems and critical groups estimates. © 2009 Juliusz Schauder Center for Nonlinear Studies. 34 1 77 89 Amann, H., Zehnder, E., Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations (1980) Ann. Scuola Norm. Sup. Pisa Cl. Sci., 4, pp. 539-603 Ambrosetti, A., Brezis, H., Cerami, G., Combined effects of concave and convex nonlinearities in some elliptic problems (1994) J. Funct. Anal., 122, pp. 519-543 Ambrosetti, A., Azorero, J.G., Peral, I., Multiplicity results for some nonlinear elliptic equations (1996) J. Funct. Anal., 137, pp. 219-242 Ambrosetti, A., Rabinowitz, P., Dual variational methods in critical point theory and applications (1973) J. Funct. Anal., 14, pp. 349-381 Anane, A., Simplicitét isolation de la première valeur propre du p-laplacien avec poids (1987) C. R. Acad. Sci. Paris Sér. I Math., 305, pp. 725-728 Benci, V., D'Avenia, P., Fortunato, D., Pisani, L., Solitons in several space dimensions: Derrick's problem and infinitely many solutions (2000) Arch. Rational Mech. Anal., 154, pp. 297-324 Benci, V., Fortunato, D., Pisani, L., Soliton like solutions of a Lorentz invariant equation in dimension 3 (1998) Rev. Math. Phys., 10, pp. 315-344 Brezis, H., Nirenberg, L., H 1 versus C 1 local minimizers (1993) C. R. Acad. Sci. Paris Sér. I Math., 317, pp. 465-472 Chang, K.C., (1993) Infinite Dimensional Morse Theory and Multiple Solution Problems, , Birkhäuser, Boston Cingolani, S., Degiovanni, M., Nontrivial solutions for p-Laplace equations with right-hand side having p-linear growth at infinity (2005) Comm. Partial Differential Equations, 30, pp. 1191-1203 Cingolani, S., Vannella, G., Critical groups computations on a class of Sobolev Banach spaces via Morse index (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire, 20, pp. 271-292 De Figueiredo, D.G., (1989) Lectures on the Ekeland Variational Principle with Applications and Detours, 81. , Tata Institute of Fundamental Research Lectures on Mathematics and Physics, Published for the Tata Institute of Fundamental Research, Bombay, Springer-Verlag, Berlin De Figueiredo, D.G., Gossez, J.P., Ubilla, P., Local superlinearity and sublinearity for indefinite semilinear elliptic problems (2003) J. Funct. Anal., 199, pp. 452-467 De Paiva, F.O., Massa, E., Multiple solutions for some elliptic equations with a nonlinearity concave at the origin (2007) Nonlinear Anal., 66, pp. 2940-2946 Díaz, J.I., Nonlinear Partial Differential Equations and Free Boundaries, Vol. I Elliptic equations (1985) Research Notes in Mathematics, 106. , Pitman, Boston, MA De Ó, J.M., Existence of solutions for quasilinear elliptic equations (1997) J. Math. Anal. Appl., 207, pp. 104-126 Azorero, J.G., Peral, I., Manfredi, J., Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations (2000) Comm. Contemp. Math., 2, pp. 385-404 Guo, Z., Zhang, Z., W 1, p versus C 1 local minimizers and multiplicity results for quasilinear elliptic equations (2003) J. Math. Anal. Appl., 286, pp. 32-50 Ladyzhenskaya, O.A., Uraltseva, N.N., (1968) Linear and Quasilinear Elliptic Equations, , Academic Press, New York Lieberman, G.M., Boundary regularity for solutions of degenerate elliptic equations (1988) Nonlinear Anal., 12, pp. 1203-1219 Perera, K., Multiplicity results for some elliptical problems with concave nonlinearities (1997) J. Differential Equations, 140, pp. 133-141 Critical groups of pair of critical points produced by linking subsets (1997) J. Differential Equations, 140, pp. 142-160 Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations (1986) CBMS Regional Conf. Ser. in Math., 65. , Amer. Math. Soc. Providence, RI Tolksdorf, P., On the Dirichlet problem for quasilinear equations in domains with conical boundary points (1983) Comm. Partial Differential Equations, 8, pp. 773-817 Ubilla, P., Multiplicity results for quasilinear elliptic equations (1996) Comm. Appl. Nonlinear Anal., 3, pp. 35-49