Title | Multiple positive solutions for a superlinear problem: a topological approach |

Publication Type | Journal Article |

Year of Publication | 2015 |

Authors | Feltrin, G, Zanolin, F |

Journal | J. Differential Equations 259 (2015), 925–963. |

Abstract | We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u''+f(x,u)=0. We allow x ↦ f(x,s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f(x,s)/s is below λ_1 as s→0^+ and above λ_1 as s→+∞. In particular, we can deal with the situation in which f(x,s) has a superlinear growth at zero and at infinity. We propose a new approach based on the topological degree which provides the multiplicity of solutions. Applications are given for u'' + a(x) g(u) = 0, where we prove the existence of 2^n-1 positive solutions when a(x) has n positive humps and a^-(x) is sufficiently large. |

URL | http://urania.sissa.it/xmlui/handle/1963/35147 |

DOI | 10.1016/j.jde.2015.02.032 |

## Multiple positive solutions for a superlinear problem: a topological approach

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