Lack of coercivity in a concave—convex type equation

Quoirin, Humberto Ramos
March 2010
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p523
Academic Journal
Existence and multiplicity of non-negative solutions are investigated for the concave–convex type equation where Ω is a bounded domain and 1 < r < p < q < p*. By minimization on the Nehari manifold, we find conditions on V, a, and b that yield up to four non-negative solutions when the left-hand side of the equation has a non-coercive behavior, a and b are sign-changing, and λ is positive and sufficiently small.


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