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Volume 8, Issue 3
Positive Solution of a Semilinear Elliptic Equation on RN

Daomin Cao

J. Part. Diff. Eq., 8 (1995), pp. 261-272.

Published online: 1995-08

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  • Abstract
In this paper, we obtain the existence of positive solution of {-Δu = b(x)(u - λ)^p_+,\qquad x ∈ R^N λ > 0, |∇ u| ∈ L² (R^N),\qquad u ∈ L\frac{2N}{N-2} (R^N) under the assumptions that 1 < p < \frac{N+2}{N-2}, N ≥ 3, b(x) satisfies b(x) ∈ C(R^N), b(x) > 0 in R^N b(x) →_{|x|→∞}b^∞ and b(x) > \frac{4}{p+3}b^∞ for x ∈ R^N
  • Keywords

Elliptic equations positive solution critical point

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@Article{JPDE-8-261, author = {Cao , Daomin}, title = {Positive Solution of a Semilinear Elliptic Equation on RN}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {3}, pages = {261--272}, abstract = { In this paper, we obtain the existence of positive solution of {-Δu = b(x)(u - λ)^p_+,\qquad x ∈ R^N λ > 0, |∇ u| ∈ L² (R^N),\qquad u ∈ L\frac{2N}{N-2} (R^N) under the assumptions that 1 < p < \frac{N+2}{N-2}, N ≥ 3, b(x) satisfies b(x) ∈ C(R^N), b(x) > 0 in R^N b(x) →_{|x|→∞}b^∞ and b(x) > \frac{4}{p+3}b^∞ for x ∈ R^N }, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5658.html} }
TY - JOUR T1 - Positive Solution of a Semilinear Elliptic Equation on RN AU - Cao , Daomin JO - Journal of Partial Differential Equations VL - 3 SP - 261 EP - 272 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5658.html KW - Elliptic equations KW - positive solution KW - critical point AB - In this paper, we obtain the existence of positive solution of {-Δu = b(x)(u - λ)^p_+,\qquad x ∈ R^N λ > 0, |∇ u| ∈ L² (R^N),\qquad u ∈ L\frac{2N}{N-2} (R^N) under the assumptions that 1 < p < \frac{N+2}{N-2}, N ≥ 3, b(x) satisfies b(x) ∈ C(R^N), b(x) > 0 in R^N b(x) →_{|x|→∞}b^∞ and b(x) > \frac{4}{p+3}b^∞ for x ∈ R^N
Cao , Daomin. (1995). Positive Solution of a Semilinear Elliptic Equation on RN. Journal of Partial Differential Equations. 8 (3). 261-272. doi:
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