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We consider the existence and nonexistence of solutions for the following singular quasi-linear elliptic problem with concave and convex nonlinearities:
⎧ , x ∈ Ω,
⎨
⎩ , x ∈ ∂Ω,
where Ω is an exterior domain in , that is, , where D is a bounded domain in with smooth boundary ∂D(=∂Ω), and 0 ∈ Ω. Here λ > 0, 0 ≤ a < (N-p)/p, 1 < p< N, ∂/∂ν is the outward normal derivative on ∂Ω. By the variational method, we prove the existence of multiple solutions. By the test function method,...
We study the existence of positive solutions of the quasilinear problem
⎧ , ,
⎨
⎩ u(x) > 0, ,
where is the N-Laplacian operator, is a continuous potential, is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.
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