Positive solutions for singular critical elliptic problems
نویسندگان
چکیده
منابع مشابه
Critical points and positive solutions of singular elliptic boundary value problems ✩
Usually we do not think there is variational structure for singular elliptic boundary value problems, so it cannot be considered by using critical points theory. In this paper, we use critical theory on certain convex closed sets to solve positive solutions for singular elliptic boundary value problems, especially use the ordinary differential equation theory of Banach spaces to obtain new resu...
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We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.
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[1] R. B. Assunção, P. C. Carrião, O. H. Miyagaki, Multiplicity of solutions for critical singular problems, Applied Mathematics Letters 19 (2006) 741–746. [2] R. B. Assunção, P. C. Carrião, O. H. Miyagaki, Critical singular problems via concentration-compactness lemma, J. Math. Anal. Appl. 326 (2007), 137–154. [3] J. Chen, S. Li, On multiple solutions of a singular quasilinear equation on unbo...
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We study an elliptic boundary-value problem with singular nonlinearity via the method of monotone iteration scheme: −∆u(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, where ∆ is the Laplacian operator, Ω is a bounded domain in RN , N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. We prove the existence and the uniqueness of positive solutions under a set of hy...
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In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2004
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(04)90082-1