Dancer, E. N.; Du, Yihong On sign-changing solutions of certain semilinear elliptic problems. (English) Zbl 0835.35051 Appl. Anal. 56, No. 3-4, 193-206 (1995). We continue our work on when the equation \(-\Delta u= f(u)\) in \(\Omega\), \(u= 0\) on \(\partial\Omega\) has a changing sign solution. Here \(\Omega\) is a bounded domain in \(\mathbb{R}^n\). In the first part, we use ideas from H. Hofer [Math. Ann. 261, 493-514 (1982; Zbl 0488.47034)] to prove the existence of changing sign solutions when \(f\) is sublinear at infinity. This improves an earlier work of the authors [J. Math. Anal. Appl. 189, No. 3, 848-871 (1995)]. In the second part, we obtain results for some superlinear subcritical problems. This depends on a variant of a result of K.-C. Chang [Infinite-dimensional Morse theory and its applications (Universite de Montreal, Canada, 1985; Zbl 0609.58001)] for the degree of maps which are of variational type. Reviewer: E.N.Dancer (Sydney) Cited in 30 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 47J25 Iterative procedures involving nonlinear operators Keywords:fixed point index; existence of changing sign solutions PDF BibTeX XML Cite \textit{E. N. Dancer} and \textit{Y. Du}, Appl. Anal. 56, No. 3--4, 193--206 (1995; Zbl 0835.35051) Full Text: DOI References: [1] DOI: 10.1137/1018114 · Zbl 0345.47044 · doi:10.1137/1018114 [2] d’Aujourdlhui M., Sur l’ensemble de resonance d’un problem demi- lineaire [3] DOI: 10.1080/03605307708820041 · Zbl 0358.35032 · doi:10.1080/03605307708820041 [4] Chang K.C., Infinite Dimensional Morse Theory and Its Applications (1985) · Zbl 0609.58001 [5] Dancer E.N., Proc. Royal Soc. Edinburgh 76 pp 283– (1977) · Zbl 0351.35037 · doi:10.1017/S0308210500019648 [6] DOI: 10.1515/crll.1984.350.1 · Zbl 0525.58012 · doi:10.1515/crll.1984.350.1 [7] DOI: 10.1016/0362-546X(91)90048-6 · Zbl 0755.47038 · doi:10.1016/0362-546X(91)90048-6 [8] DOI: 10.1016/0022-0396(90)90005-A · Zbl 0729.35050 · doi:10.1016/0022-0396(90)90005-A [9] DOI: 10.1515/crll.1986.371.46 · Zbl 0597.47034 · doi:10.1515/crll.1986.371.46 [10] Dancer E.N., to appear in J. Diff. Eqns. [11] Dancer, E.N. and Dul, Y. ”Existence of changing sign solutions for some semilinear problems with juiping nonlinearities at zero”. Edinburgh. to appear in Proc. Royal Soc. [12] Dancer E.N., to appear in J. Math. Anal. Appl [13] Dancer E.N., to appear in Comm. Applied Nonlinear Analysis. [14] Deimling K., Nonlinear Functional Analysis (1985) · Zbl 0559.47040 · doi:10.1007/978-3-662-00547-7 [15] de Figueiredo D.G., J. Math. Pures et Appl. 61 pp 41– (1982) [16] Fucik S., Casopis Pest. Mat. 101 pp 69– (1976) [17] DOI: 10.1080/03605308108820196 · Zbl 0462.35041 · doi:10.1080/03605308108820196 [18] Gilbarg D., Elliptic Partial Differential Equations of Second Order (1977) · Zbl 0361.35003 · doi:10.1007/978-3-642-96379-7 [19] DOI: 10.1090/S0002-9939-1984-0727256-0 · doi:10.1090/S0002-9939-1984-0727256-0 [20] DOI: 10.1007/BF01457453 · Zbl 0488.47034 · doi:10.1007/BF01457453 [21] Krasnoselskii M.A., Noordhoff (1964) [22] Nussbaum R.D., Ann. Mat. Pura. Appl. 87 pp 217– (1971) · Zbl 0226.47031 · doi:10.1007/BF02414948 [23] Rabinowitz P.H., CBMS Ser. in Math. 65 (1986) [24] Sweers G., Progress in Partial Differential Equations pp 251– (1992) [25] Wang Z.Q., Ann. Inst. Henri Poincare 8 pp 43– (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.