Artículos de revistas
Pairs Of Solutions Of Asymptotically Linear Elliptic Problems
Registro en:
Communications In Applied Analysis. , v. 13, n. 3, p. 375 - 384, 2009.
10832564
2-s2.0-70350022404
Autor
De Paiva F.O.
Institución
Resumen
We establish the existence of two nontrivial solutions for the semilinear elliptic problem -Δu = g(x, u) in Ω u = 0 on ∂Ω, where Ω ⊂ RN is a smooth bounded domain, g €C1 (Ω × R \{0},R) is such that g(x,0) = 0 and asymptotically linear. Our proofs are based on minimax methods and critical groups. ©Dynamic Publishers, Inc. 13 3 375 384 Ahmad, S., Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems (1987) Proc. Amer. Math. Soc., 96, pp. 405-409 Ambrosetti, A., Mancini, G., Sharp nonuniqueness results for some nolinear problems (1979) Nonlinear Anal., 5, pp. 635-645 Bartsch, T., Chang, K.C., Wang, Z.-Q., On the Morse indices of sign changing solutions of nonlinear elliptic problems (2000) Math. Z, 233, pp. 655-677 Bartsch, T., Li, S., Critical point theory for asymptotically quadratic functionals and applications to problems with resonance (1997) Nonlinear Anal., 28, pp. 419-441 Castro, A., Lazer, A.C., Critical Point Theory and the Number of Solutions of a Nonlinear Dirichlet Problem (1979) Ann. Mat. Pura Appl., 120, pp. 113-137 Chang, K.C., (1993) Infinite Dimensional Morse Theory and Multiple Solutions Problems, , Birkhäuser, Boston Dancer, D.N., Zhang, Z., Fucik Spectrum, Sign-Changing, and Multiple Solutions for Semilinear Elliptic Boundary Value Problems with Resonance at infinity (2000) J. Math. Anal. Appl., 250, pp. 449-464 De Figueiredo, D.G., Positive Solutions of Semilinear Elliptic Problems (1982) Lectures Notes in Math., 957, pp. 34-87 Hirano, N., Multiple nontrivial solutions of semilinear elliptic equations (1988) Proc. Amer. Math. Soc., 103, pp. 468-472 Hirano, N., Existence of nontrivial solutions of semilinear elliptic equations (1989) Nonlinear Anal., 13, pp. 695-705 Hirano, N., Nishimura, T., Multiple results for semilinear elliptic problems at resond with jumping nonlinearities (1988) Proc. Amer. Math. Soc., 103, pp. 468-472 Li, C., Li, S.-J., Liu, J.-Q., Splitting theorem, Poincar-Hopf theorem and jumping nonlinear problems (2005) J. Funct. Anal., 221, pp. 439-455 Li, S.-J., Perera, K., Su, J.-B., Computation of Critical Groups in Boundary Value Problems where the Asymptotic Limit may not Exist (2001) Proc. Roy. Soc. Edinburgh Sect. A, 131, pp. 721-723 Li, S.-J., Su, J.-B., Existense of Multiple Solutions of a Two-Point Boundary Value Problems (1997) Topol. Methods Nonlinear Anal., 10, pp. 123-135 Li, S.-J., Willem, M., Multiple solutions for asymptotically linear boundary value problems in which the nonlinearity crosses at least one eigenvalue (1998) NoDEA Nonlinear Differential Equations Appl., 5, pp. 479-490 Liu, J.Q., (1989) A Morse Index for A Saddle Point Syst. Sc. and Math. Sc., 2, pp. 32-39 Mizoguchi, N., Multiple Nontrivial Solutions of Semilinear Elliptic Equations and their Homo-topy Indices (1994) J. Differential Equations, 108, pp. 101-119 De Paiva, F.O., Multiple Solutions for Asymptotically Linear Ressonant Elliptics Problems (2003) Topol. Methods Nonlinear Anal., 21, pp. 227-247 De Paiva, F.O., Multiple solutions for elliptic problems with asymmetric nonlinearity (2004) J. Math. Anal. Appl., 292, pp. 317-327 Perera, K., Multiplicity results for some elliptical problems with concave nonlinearities (1997) J. Differential Equations, 140, pp. 133-141 Zou, W., Multiple Solutions Results for Two-Point Boundary Value Problems with Resonance (1998) Discret Contin. Dyn. Syst., 4, pp. 485-496