Concave-Convex Problems for the Robin p-Laplacian Plus an Indefinite Potential
Keyword(s):
We consider nonlinear Robin problems driven by the p-Laplacian plus an indefinite potential. In the reaction, we have the competing effects of a parametric concave (that is, ( p − 1 ) -sublinear) term and of a convex (that is, ( p − 1 ) -superlinear) term which need not satisfy the Ambrosetti–Rabinowitz condition. We prove a "bifurcation-type" theorem describing in a precise way the dependence the dependence of the set of positive solutions on the parameter λ > 0 . In addition, we show the existence of a smallest positive solution u λ * and determine the monotonicity and continuity properties of the map λ ↦ u λ * .
Keyword(s):
2019 ◽
Vol 39
(2)
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pp. 227-245
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Keyword(s):
2006 ◽
Vol 11
(4)
◽
pp. 323-329
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