Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent
We study existence of a nontrivial solution of -Δpu(x)+u(x)p-1=u(x)q(x)-1, u(x)≥0, x∈RN, u∈Wrad1,p(RN), under some conditions on q(x), especially, lim inf|x|→∞ q(x)=p. Concerning this problem, we firstly consider compactness and noncompactness for the embedding from Wrad1,p(RN) to Lq(x)(RN). We p...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5497172 |
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| author | Masato Hashizume Megumi Sano |
| author_facet | Masato Hashizume Megumi Sano |
| author_sort | Masato Hashizume |
| collection | DOAJ |
| description | We study existence of a nontrivial solution of -Δpu(x)+u(x)p-1=u(x)q(x)-1, u(x)≥0, x∈RN, u∈Wrad1,p(RN), under some conditions on q(x), especially, lim inf|x|→∞ q(x)=p. Concerning this problem, we firstly consider compactness and noncompactness for the embedding from Wrad1,p(RN) to Lq(x)(RN). We point out that the decaying speed of q(x) at infinity plays an essential role on the compactness. Secondly, by applying the compactness result, we show the existence of a nontrivial solution of the elliptic equation. |
| format | Article |
| id | doaj-art-87df06c203f842988cfd244481649869 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-87df06c203f842988cfd2444816498692025-02-03T05:57:37ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/54971725497172Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical ExponentMasato Hashizume0Megumi Sano1Graduate School of Science and Engineering, Ehime University, 10-13 Dougohimata, Matsuyama-shi, Ehime-ken 790-8577, JapanDepartment of Mathematics, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8551, JapanWe study existence of a nontrivial solution of -Δpu(x)+u(x)p-1=u(x)q(x)-1, u(x)≥0, x∈RN, u∈Wrad1,p(RN), under some conditions on q(x), especially, lim inf|x|→∞ q(x)=p. Concerning this problem, we firstly consider compactness and noncompactness for the embedding from Wrad1,p(RN) to Lq(x)(RN). We point out that the decaying speed of q(x) at infinity plays an essential role on the compactness. Secondly, by applying the compactness result, we show the existence of a nontrivial solution of the elliptic equation.http://dx.doi.org/10.1155/2018/5497172 |
| spellingShingle | Masato Hashizume Megumi Sano Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent Journal of Function Spaces |
| title | Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent |
| title_full | Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent |
| title_fullStr | Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent |
| title_full_unstemmed | Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent |
| title_short | Strauss’s Radial Compactness and Nonlinear Elliptic Equation Involving a Variable Critical Exponent |
| title_sort | strauss s radial compactness and nonlinear elliptic equation involving a variable critical exponent |
| url | http://dx.doi.org/10.1155/2018/5497172 |
| work_keys_str_mv | AT masatohashizume strausssradialcompactnessandnonlinearellipticequationinvolvingavariablecriticalexponent AT megumisano strausssradialcompactnessandnonlinearellipticequationinvolvingavariablecriticalexponent |