Bounded Solutions for Non-parametric Mean Curvature Problems with Nonlinear Terms
Bounded Solutions for Non-parametric Mean Curvature Problems with Nonlinear Terms
Abstract In this paper we prove existence of nonnegative bounded solutions for the non-autonomous prescribed mean curvature problem in non-parametric form on an open bounded domain $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Ω</mml:mi> </mml:math> of $${{\,\mathrm{\mathbb {R}}\,}}^N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mrow> <mml:mspace/> <mml:mi>R</mml:mi> <mml:mspace/> </mml:mrow> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> </mml:math> . The …