Castro, Alfonso; Cossio, Jorge Multiple radial solutions for a semilinear Dirichlet problem in a ball. (English) Zbl 0799.35024 Rev. Colomb. Mat. 27, No. 1-2, 15-24 (1993). The authors prove that the semilinear elliptic boundary value problem \(\Delta u+ f(u)=0\) in \(\Omega\), \(u=0\) on \(\partial\Omega\) has at least \(4j-1\) radially symmetric solutions if the nonlinearity has a positive zero and satisfies \(f(0)=0\), \(f'(0)= f'(\infty) >\lambda_ j\), where \(\lambda_ 1< \lambda_ 2<\dots\) are the eigenvalues of \(-\Delta\) in the space of radial functions of \(H_ 0^ 1(\Omega)\). Extensive use is made of the global bifurcation theorem, bifurcation from infinity and bifurcation from simple eigenvalues. Cited in 4 Documents MSC: 35B32 Bifurcations in context of PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:semilinear elliptic boundary value problem; bifurcation from infinity; bifurcation from simple eigenvalues PDFBibTeX XMLCite \textit{A. Castro} and \textit{J. Cossio}, Rev. Colomb. Mat. 27, No. 1--2, 15--24 (1993; Zbl 0799.35024) Full Text: EuDML