Abstract
We deal with the existence of positive solutions u decaying to zero at infinity, for a class of equations of Lane–Emden–Fowler type involving a gradient term. One of the main points is that the differential equation contains a semilinear term σ ( u ) where σ : ( 0 , ∞ ) → ( 0 , ∞ ) is a smooth function which can be both unbounded at infinity and singular at zero. Our technique explores symmetry arguments as well as lower and upper solutions.
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