Schechter, Martin A generalization of the saddle point method with applications. (English) Zbl 0780.35001 Ann. Pol. Math. 57, No. 3, 269-281 (1992). The saddle theorem considers a continuous \(G\) differentiable functional in a Hilbert space \(H\), satisfying \(\inf\{G(v)\), \(v\in M\}=m_ 0>- \infty\), \(\limsup G(v)=m<+\infty\) for \(v\in N\) and \(\| v\|\to+\infty\) where \(H=M+N\) is an orthogonal decomposition of \(H\) into closed subspaces \(M\) and \(N\) with \(\dim N<+\infty\). The theorem states that if \(m<m_ 0\) there exist \(c\geq m_ 0\) and a sequence \((u_ k)\) in \(H\) such that \(G(u_ k)\to c\) and \(G'(u_ k)\to 0\).In this paper the author shows that the condition \(m<m_ 0\) is unnecessary and obtains the same result even if \(m\geq m_ 0\). Some interesting applications on the existence of solutions for boundary value problems are also given. Reviewer: E.Mascolo (Firenze) Cited in 2 ReviewsCited in 15 Documents MSC: 35A15 Variational methods applied to PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:saddle point method; existence; boundary value problems PDFBibTeX XMLCite \textit{M. Schechter}, Ann. Pol. Math. 57, No. 3, 269--281 (1992; Zbl 0780.35001) Full Text: DOI