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Keywords:
sign-changing; mountain-pass theorem; ordered intervals
sign-changing; mountain-pass theorem; ordered intervals
Summary:
In this paper we show some results of multiplicity and existence of sign-changing solutions using a mountain pass theorem in ordered intervals, for a class of quasi-linear elliptic Dirichlet problems. As a by product we construct a special pseudo-gradient vector field and a negative pseudo-gradient flow for the nondifferentiable functional associated to our class of problems.
References:
[1] Alama S., Del Pino M.: Solutions of elliptic equation with indefinite nonlinearities via Morse theory and linking. Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 95-115. MR 1373473
[2] Alama S., Tarantello G.: On semilinear elliptic equations with indefinite nonlinearities. Calc. Var. Partial Differential Equations 1 (1993), 469-475. MR 1383913 | Zbl 0809.35022
[3] Amann H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976), 620-709. MR 0415432 | Zbl 0345.47044
[4] Ambrosetti A., Brezis H., Cerami G.: Combined effects of concave and convex nonlinearities in some elliptic problems. J. Funct. Anal. 122 (1994), 519-543. MR 1276168 | Zbl 0805.35028
[5] Ambrosetti A., Azorero J.G., Peral I.: Multiplicity results for some nonlinear elliptic equations. J. Funct. Anal. 137 (1996), 214-242. MR 1383017 | Zbl 0852.35045
[6] Ambrosetti A., Azorero J.G., Peral I.: Existence and multiplicity results for some nonlinear elliptic equations. a survey, SISSA preprint 4/2000/M. MR 1801341 | Zbl 1011.35049
[7] Arcoya D., Boccardo L.: Some remarks on critical point theory for nondifferentiable functionals. Nonlinear Differential Equations Appl. 6 (1999), 79-100. MR 1674782 | Zbl 0923.35049
[8] Arcoya D., Carmona J., Pellacci B.: Bifurcation for some quasi-linear operators. SISSA preprint, 1999.
[9] Artola M., Boccardo L.: Positive solutions for some quasi-linear elliptic equations. Comm. Appl. Nonlinear Anal. 3 4 (1996), 89-98. MR 1420287
[10] Chang K.C.: Infinite dimensional Morse theory and multiple solution problems. Birkhäuser, Boston, 1993. MR 1196690 | Zbl 0779.58005
[11] Chang K.C.: $H^1$ versus $C^1$ isolated critical points. C.R. Acad. Sci. Paris, Sér. I Math. 319 441-446 (1994). MR 1296769
[12] Dancer E.N., and Du Yihong: A note on multiple solutions for some semilinear elliptic problems. J. Math. Anal. Appl. 211 (1997), 626-640. MR 1458519
[13] de Figueiredo D.G.: Positive solutions of semilinear elliptic problems. in Variational Methods in Analysis and Mathematical Physics, ICTP Trieste autumn course, 1981. Zbl 0506.35038
[14] Mawhin J., Willem M.: Critical point theory and Hamiltonian Systems. Springer, New York, 1989. MR 0982267 | Zbl 0676.58017
[15] Li. S., Wang Z.Q.: Mountain-pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet's problems. J. Anal. Math. 81 (2000), 373-395. MR 1785289
[16] Li S., Zhang Z.: Sign-changing solutions ad multiple solution theorems for semilinear elliptic boundary value problems with jumping nonlinearities. Acta Math. Sinica 16 1 (2000), 113-122. MR 1760528
[17] Struwe M.: Variational Methods: Applications to Nonlinear Partial Differential Equation and Hamiltonian Systems. Springer, Berlin, 1990. MR 1078018
[18] Whyburn G.T.: Topological Analysis. Princeton University Press, Princeton, 1958. MR 0099642 | Zbl 0186.55901
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