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<p>This paper deals with a class of nonlinear elliptic equations in an unbounded domain <mml:math alttext="$D$">   <mml:mi>D</mml:mi> </mml:math> of <mml:math alttext="${mathbb{R}}^n$">   <mml:msup>    <mml:mi>&#x211D;</mml:mi>    <mml:mi>n</mml:mi>   </mml:msup> </mml:math>, <mml:math alttext="$n geq 3$">   <mml:mi>n</mml:mi><mml:mo>&#x2265;</mml:mo><mml:mn>3</mml:mn> </mml:math>, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class <mml:math alttext="$K^{infty}(D)$">   <mml:msup>    <mml:mi>K</mml:mi>    <mml:mi>&#x221E;</mml:mi>   </mml:msup>   <mml:mrow><mml:mo>(</mml:mo>    <mml:mi>D</mml:mi>   <mml:mo>)</mml:mo></mml:mrow> </mml:math>. Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem.</p

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Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="${\mathbb{R}}^n$" id="E1"><mml:msup><mml:mi>ℝ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math>

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