Classical and Weak Solutions of a Singular Semilinear Elliptic Problem
The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution in Rn that decays to zero at ∞ if p(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0 t max|x| = t p(x) dt < ∞, provided f is a non-increasing continuously diff...
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AFIT Scholar
1997
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| On-line přístup: | https://scholar.afit.edu/facpub/259 https://www.sciencedirect.com/science/article/pii/S0022247X97954706/pdfft?md5=c7911d1870c051588f16dda8418089fc&pid=1-s2.0-S0022247X97954706-main.pdf |
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| _version_ | 1870452953401262080 |
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| author | Lair, Alan V. Shaker, Aihua W. |
| author_facet | Lair, Alan V. Shaker, Aihua W. |
| author_sort | Lair, Alan V. |
| building | US Air Force Institute of Technology (AFIT) |
| collection | AFIT Scholar |
| description | The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution in Rn that decays to zero at ∞ if p(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0 t max|x| = t p(x) dt < ∞, provided f is a non-increasing continuously differentiable function on (0, ∞). It is also shown that the equation has a unique weakH10-solution on a bounded domain provided ∫ε0 f(s) ds < ∞ and p(x) ∈ L2. |
| format | text |
| id | afit-facpub-1265 |
| institution | US Air Force Institute of Technology |
| publishDate | 1997 |
| publisher | AFIT Scholar |
| record_format | dspace |
| spelling | afit-facpub-1265 Classical and Weak Solutions of a Singular Semilinear Elliptic Problem Lair, Alan V. Shaker, Aihua W. The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution in Rn that decays to zero at ∞ if p(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0 t max|x| = t p(x) dt < ∞, provided f is a non-increasing continuously differentiable function on (0, ∞). It is also shown that the equation has a unique weakH10-solution on a bounded domain provided ∫ε0 f(s) ds < ∞ and p(x) ∈ L2. 1997-07-15T07:00:00Z text https://scholar.afit.edu/facpub/259 info:doi/<a href="https://doi.org/10.1006/jmaa.1997.5470">10.1006/jmaa.1997.5470</a> https://www.sciencedirect.com/science/article/pii/S0022247X97954706/pdfft?md5=c7911d1870c051588f16dda8418089fc&pid=1-s2.0-S0022247X97954706-main.pdf Faculty Publications AFIT Scholar Elliptical problems 35J65 Partial Differential Equations |
| spellingShingle | Elliptical problems 35J65 Partial Differential Equations Lair, Alan V. Shaker, Aihua W. Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title | Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title_full | Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title_fullStr | Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title_full_unstemmed | Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title_short | Classical and Weak Solutions of a Singular Semilinear Elliptic Problem |
| title_sort | classical and weak solutions of a singular semilinear elliptic problem |
| topic | Elliptical problems 35J65 Partial Differential Equations |
| url | https://scholar.afit.edu/facpub/259 https://www.sciencedirect.com/science/article/pii/S0022247X97954706/pdfft?md5=c7911d1870c051588f16dda8418089fc&pid=1-s2.0-S0022247X97954706-main.pdf |
| work_keys_str_mv | AT lairalanv classicalandweaksolutionsofasingularsemilinearellipticproblem AT shakeraihuaw classicalandweaksolutionsofasingularsemilinearellipticproblem |