Positive solutions for parametric semilinear Robin problems with indefinite and unbounded potential
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We consider a parametric Robin problem driven by the Laplace operator plus an indefinite and unbounded potential. The reaction term is a Carathéodory function which exhibits superlinear growth near $+\infty $ without satisfying the Ambrosetti-Rabinowitz condition. We are looking for positive solutions and prove a bifurcation-type theorem describing the dependence of the set of positive solutions on the parameter. We also establish the existence of the minimal positive solution $u^*_{\lambda }$ and investigate the monotonicity and continuity properties of the map $\lambda \mapsto u^*_{\lambda }$.
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2007 ◽
Vol 52
(10-11)
◽
pp. 945-977
◽
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2017 ◽
Vol 21
(6)
◽
pp. 135-140
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