Budd, C.; Knaap, M. C.; Peletier, L. A. Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions. (English) Zbl 0733.35038 Proc. R. Soc. Edinb., Sect. A 117, No. 3-4, 225-250 (1991). From the authors’ introduction: “In this paper we shall study non- constant radially symmetric solutions of the problem \[ (I)\quad -\Delta u=\lambda (u^ p-u^ q)\text{ in } B,\quad u>0\text{ in } B,\quad \partial u/\partial n=0\text{ on } \partial B, \] where B is the unit ball in \({\mathbb{R}}^ N\) \((N>2)\) and n is the outward pointing normal, \(p=(N+2)/(N-2)\), \(0<q<p-1=4/(N-2)\). In addition we shall only consider those solutions of Problem (I) which are decreasing in \(r=| x|\).” Reviewer: M.Chicco (Genova) Cited in 26 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:critical exponent; Neumann problem; semilinear equation; radially symmetric solutions PDFBibTeX XMLCite \textit{C. Budd} et al., Proc. R. Soc. Edinb., Sect. A, Math. 117, No. 3--4, 225--250 (1991; Zbl 0733.35038) Full Text: DOI References: [1] DOI: 10.1016/0022-1236(73)90051-7 · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7 [2] Atkinson, Asymptotic Anal. 1 pp 139– (1988) [3] DOI: 10.1016/0362-546X(86)90036-2 · Zbl 0662.34024 · doi:10.1016/0362-546X(86)90036-2 [4] DOI: 10.1090/S0002-9947-1985-0808736-1 · doi:10.1090/S0002-9947-1985-0808736-1 [5] DOI: 10.1216/RMJ-1973-3-2-161 · Zbl 0255.47069 · doi:10.1216/RMJ-1973-3-2-161 [6] DOI: 10.1002/cpa.3160360405 · Zbl 0541.35029 · doi:10.1002/cpa.3160360405 [7] DOI: 10.1007/BF01460131 · Zbl 0527.35026 · doi:10.1007/BF01460131 [8] Lin, On the diffusion coefficient of a semilinear Neumann problem (1986) [9] DOI: 10.1016/0022-5193(70)90092-5 · Zbl 1170.92306 · doi:10.1016/0022-5193(70)90092-5 [10] Budd, Proc. Roy. Soc. Edinburgh Sect. A 107 pp 249– (1987) · Zbl 0662.35003 · doi:10.1017/S0308210500031140 [11] DOI: 10.1016/0022-0396(88)90147-7 · Zbl 0676.35030 · doi:10.1016/0022-0396(88)90147-7 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.