{"id":40975,"date":"2024-09-25T09:32:29","date_gmt":"2024-09-25T09:32:29","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d8%a7%d9%87-%d8%ad%d9%84-%d9%87%d8%a7%db%8c-%d8%ba%db%8c%d8%b1-%d9%85%d9%86%d9%81%db%8c-%db%8c%da%a9\/"},"modified":"2024-09-25T09:32:30","modified_gmt":"2024-09-25T09:32:30","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d8%a7%d9%87-%d8%ad%d9%84-%d9%87%d8%a7%db%8c-%d8%ba%db%8c%d8%b1-%d9%85%d9%86%d9%81%db%8c-%db%8c%da%a9","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d8%a7%d9%87-%d8%ad%d9%84-%d9%87%d8%a7%db%8c-%d8%ba%db%8c%d8%b1-%d9%85%d9%86%d9%81%db%8c-%db%8c%da%a9\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0645\u0646\u0641\u06cc \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u0628\u06cc\u0636\u0648\u06cc \u0632\u06cc\u0631\u062e\u0637\u06cc"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nNon-negative solutions of a sublinear elliptic problem<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0645\u0646\u0641\u06cc \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u0628\u06cc\u0636\u0648\u06cc \u0632\u06cc\u0631\u062e\u0637\u06cc<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nJuli\u00e1n L\u00f3pez-G\u00f3mez, Paul H. Rabinowitz, Fabio Zanolin<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n25<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nAnalysis of PDEs,\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 PDES ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 7 March, 2024; originally announced March 2024. , Comments: 25 pages, 11 figures , MSC Class: 35B09; 35B25; 35B32; 35J15<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 7 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 25 \u0635\u0641\u062d\u0647 \u060c 11 \u0634\u06a9\u0644 \u060c \u06a9\u0644\u0627\u0633 MSC: 35B09 \u061b35B25 \u061b35B32 \u061b35J15<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In this paper the existence of solutions, $(\u03bb,u)$, of the problem $$-\u0394u=\u03bbu -a(x)|u|^{p-1}u \\quad \\hbox{in }\u03a9, \\qquad u=0 \\quad \\hbox{on}\\;\\;\\partial\u03a9,$$ is explored for $0 < p < 1$. When $p>1$, it is known that there is an unbounded component of such solutions bifurcating from $(\u03c3_1, 0)$, where $\u03c3_1$ is the smallest eigenvalue of $-\u0394$ in $\u03a9$ under Dirichlet boundary conditions on $\\partial\u03a9$. These solutions have $u \\in P$, the interior of the positive cone. The continuation argument used when $p>1$ to keep $u \\in P$ fails if $0 < p < 1$. Nevertheless when $0 < p < 1$, we are still able to show that there is a component of solutions bifurcating from $(\u03c3_1, \\infty)$, unbounded outside of a neighborhood of $(\u03c3_1, \\infty)$, and having $u \\gneq 0$. This non-negativity for $u$ cannot be improved as is shown via a detailed analysis of the simplest autonomous one-dimensional version of the problem: its set of non-negative solutions possesses a countable set of components, each of them consisting of positive solutions with a fixed (arbitrary) number of bumps. Finally, the structure of these components is fully described.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0648\u062c\u0648\u062f \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627 \u060c $ (\u03bb \u060c u) $ \u060c \u0627\u0632 \u0645\u0634\u06a9\u0644 $ $-\u0394U = \u03bbu -a (x) | u |^{p-1} u \\ quad \\ hbox {in} \u03c9 \u060c \\qquad u = 0 \\ quad \\ hbox {on} \\ \u061b \\ \u061b \\ partial\u03a9 \u060c $ $ \u0628\u0627 \u0642\u06cc\u0645\u062a 0 $ <\/p>\n

1 $ \u060c \u0645\u0634\u062e\u0635 \u0634\u062f\u0647 \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0645\u0624\u0644\u0641\u0647 \u0628\u062f\u0648\u0646 \u0645\u0631\u0632 \u0627\u0632 \u0686\u0646\u06cc\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0627\u0632 $ (\u03c3_1 \u060c 0) $ \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 $ \u03c3_1 $ \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u06cc\u0698\u0647 $ $ \u062f\u0631 $ \u03c9 $ \u062f\u0631 \u0634\u0631\u0627\u06cc\u0637 \u0645\u0631\u0632\u06cc Dirichlet \u0627\u0633\u062a.\u062f\u0631 $ \\ partial\u03a9 $.\u0627\u06cc\u0646 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627 \u062f\u0627\u0631\u0627\u06cc u \\ u \\ \u062f\u0631 p $ \u060c \u0641\u0636\u0627\u06cc \u062f\u0627\u062e\u0644\u06cc \u0645\u062e\u0631\u0648\u0637 \u0645\u062b\u0628\u062a \u0627\u0633\u062a.\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u062f\u0627\u0645\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 $ p> 1 $ \u0628\u0631\u0627\u06cc \u0646\u06af\u0647 \u062f\u0627\u0634\u062a\u0646 $ u \\ in p $ \u0627\u06af\u0631 0 \u062f\u0644\u0627\u0631 <\/p>\n

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