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Branches of positive solutions of subcritical elliptic equations in convex domains

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  • We provide sufficient conditions for the existence of $L^{\infty}$ a priori estimates for positive solutions to a class of subcritical elliptic equations in bounded $C^2$ convex domains. These sufficient conditions widen the range of nonlinearities for which a priori bounds are known. Using these a priori bounds we prove the existence of positive solutions for a class of problems depending on a parameter
    Mathematics Subject Classification: Primary: 35B45; Secondary: 35B09, 35B33, 35J25, 35J60.


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