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Bifurcation of radial solutions for prescribed mean curvature equations

N. B. Zographopoulos

Abstract

We prove global bifurcation results for prescribed mean curvature equations. These equations are defined on R3 and the radial solutions belonging in these branches are smooth and positive.

Bifurcation of radial solutions for prescribed mean curvature equations

Abstract

We prove global bifurcation results for prescribed mean curvature equations. These equations are defined on R3 and the radial solutions belonging in these branches are smooth and positive.
Paper Structure (6 sections, 16 theorems, 133 equations)

This paper contains 6 sections, 16 theorems, 133 equations.

Table of Contents

  1. Introduction
  2. Eigenvalue problems
  3. Proof of Theorem \ref{['seigen']}
  4. Proof of Proposition \ref{['mainprop']}
  5. Bifurcation Results
  6. Bifurcation for The Mean Curvature Equations

Key Result

THEOREM 1.1

Assume that $X$ is a Banach space with norm $||\cdot||$ and consider $G(\lambda,\cdot)= L(\lambda,\cdot) + H(\lambda,\cdot)$, where $L$ is a compact linear map on $X$ and $H(\lambda,\cdot)$ is compact and satisfies If $\lambda$ is a simple eigenvalue of $L$ then the closure of the set possesses a maximal continuum (i.e. connected branch) of solutions, $\mathcal{C}_\lambda$, such that $(\lambda,0

Theorems & Definitions (18)

  • THEOREM 1.1
  • THEOREM 1.2
  • PROPOSITION 1.1
  • THEOREM 1.3
  • THEOREM 1.4
  • THEOREM 1.5
  • LEMMA 2.1
  • LEMMA 2.2
  • LEMMA 2.3
  • LEMMA 2.4
  • ...and 8 more