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By construction sub and supersolutions for the followingsemilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn which arises in population genetics, wederive some results about the theory of existence of solutions aswell as asymptotic properties of the solutions for every n and for the function g:ℝn→ℝ such that g is smooth and is negative at infinity

international journal of mathematics and mathematical sciences

Super and subsolutions for elliptic equations on all of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\mathbb{R}^n$"><mml:mrow><mml:msup><mml:mi>ℝ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:math>

Super and subsolutions for elliptic equations on all ofℝn