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Existence of Solutions for Semilinear Nonlocal Elliptic Problems via a Bolzano Theorem |
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| Authors: | David Arcoya Tommaso Leonori Ana Primo |
| Affiliation: | 1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071, Granada, Spain 2. Departamento de Matemáticas, Universidad Carlos III, Avda. de la Universidad 30, 28911, Leganés, Madrid, Spain 3. ICMAT, Instituto de Ciencias Matemáticas, Campus Cantoblanco, Calle Nicolás Cabrera 13-15, 28049, Madrid, Spain |
| Abstract: | In this paper we deal with the existence of positive solutions for the following nonlocal type of problems $$everymath{displaystyle} left{ begin{array}{l@{quad}l} -Delta u = frac{sigma}{( int_{varOmega} g(u), dx )^p} f(u) & mbox{in} varOmega, [3mm] u>0 & mbox{in} varOmega, [1mm] u=0 & mbox{on} partialvarOmega, end{array} right. $$ where Ω is a bounded smooth domain in ? N (N≥1), f,g are continuous positive functions, σ>0 and p∈?. We give sufficient conditions on the functions f and g in order to have existence of positive solutions. |
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