Existence of Multiple Positive Solutions to Some Semipositone Systems
نویسنده
چکیده
In this paper we use the method of upper and lower solutions combined with degree theoretic techniques to prove the existence of multiple positive solutions to semipositone superlinear systems of the form −∆u = g1(x, u, v) −∆v = g2(x, u, v) on a smooth, bounded domain Ω ⊂ R with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical, superlinear problems with a certain concave-convex shape to their nonlinearity.
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