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Journal ArticleDOI

Nonlinear sturm‐lionville problems for second order ordinary differential equations

01 Nov 1970-Communications on Pure and Applied Mathematics (Wiley Subscription Services, Inc., A Wiley Company)-Vol. 23, Iss: 6, pp 939-961
About: This article is published in Communications on Pure and Applied Mathematics.The article was published on 1970-11-01. It has received 119 citations till now. The article focuses on the topics: Oscillation theory & Stochastic partial differential equation.
Citations
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Journal ArticleDOI
TL;DR: In this paper, general existence theorems for critical points of a continuously differentiable functional I on a real Banach space are given for the case in which I is even.

4,081 citations

Journal ArticleDOI
TL;DR: In this article, a general version of the main problem of bifurcation theory, given p ϵ C, determine the structure of G−1{0} in some neighborhood of p.

1,817 citations

Journal ArticleDOI
TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.

1,749 citations

Journal ArticleDOI
TL;DR: In this paper, the authors obtained a formula for the index in K of a fixed point of A under the assumption that a linearization exists and satisfies an invertibility condition, and used this formula to generalize some results of Amann on the number of fixed points of A to the case where K has empty interior.

204 citations

Journal ArticleDOI
TL;DR: In this article, the exact number of solutions for semi-linear elliptic problems is computed for concave and convex nonlinear problems, based on simple eigenvalue comparison arguments.

202 citations

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