%0 Journal Article %J Rev. Mat. Iberoamericana 20 (2004) 611-626 %D 2004 %T Existence of H-bubbles in a perturbative setting %A Paolo Caldiroli %A Roberta Musina %X Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. %B Rev. Mat. Iberoamericana 20 (2004) 611-626 %I SISSA Library %G en %U http://hdl.handle.net/1963/1606 %1 2512 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002