We study the existence of multiple positive solutions of −∆u = λu−q + up in Ω with homogeneous Dirichlet boundary condition, where Ω is a bounded domain in N , λ > 0 and 0 < q ≤ 1 < p ≤ (N + 2)/(N − 2). We show by variational method that if λ is less than some positive constant then the problem has at least two positive weak solutions including the cases of q = 1 or p = (N + 2)/(N − 2). We also study the regularity of positive weak solutions.
Multiple Existence of Positive Solutions for Singular Elliptic Problems with Concave and Convex Nonlinearities
SACCON, CLAUDIO;
2004-01-01
Abstract
We study the existence of multiple positive solutions of −∆u = λu−q + up in Ω with homogeneous Dirichlet boundary condition, where Ω is a bounded domain in N , λ > 0 and 0 < q ≤ 1 < p ≤ (N + 2)/(N − 2). We show by variational method that if λ is less than some positive constant then the problem has at least two positive weak solutions including the cases of q = 1 or p = (N + 2)/(N − 2). We also study the regularity of positive weak solutions.File in questo prodotto:
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