Теоремы существования для одного класса систем, содержащих два квазилинейных оператора
- Авторы: Ковеи Д.1
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Учреждения:
- The Bucharest Uviversity of Economic Studies
- Выпуск: Том 83, № 1 (2019)
- Страницы: 59-74
- Раздел: Статьи
- URL: https://journals.rcsi.science/1607-0046/article/view/133765
- DOI: https://doi.org/10.4213/im8731
- ID: 133765
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Аннотация
Изучаются вопросы существования положительных радиальных решений дляквазилинейных систем вида$$\begin{cases}\Delta_{\phi_1}u=a_1(|x|)f_1(v),\Delta_{\phi_2}v=a_2(|x|)f_2(u),\end{cases}\quad x\in \mathbb{R}^N, \quad N\ge 3,$$где $\Delta_{\phi}w:=\operatorname{div}(\phi(|\nabla w|)\nabla w)$, при надлежащих условиях на функции $\phi_1$, $\phi_2$, веса $a_1$, $a_2$ и нелинейности $f_1,$ $f_2$. Предлагаемые нами условия существования решений рассматриваемых систем отличаются от условий из предыдущих результатов.Библиография: 31 наименование.
Об авторах
Драгош-Патру Ковеи
The Bucharest Uviversity of Economic Studiesдоктор физико-математических наук, доцент
Список литературы
- D.-P. Covei, “On the radial solutions of a system with weights under the Keller–Osserman condition”, J. Math. Anal. Appl., 447:1 (2017), 167–180
- D. P. Covei, “A remark on the existence of entire large and bounded solutions to a $(k_1,k_2)$-Hessian system with gradient term”, Acta Math. Sin. (Engl. Ser.), 33:6 (2017), 761–774
- B. Franchi, E. Lanconelli, J. Serrin, “Existence and uniqueness of nonnegative solutions of quasilinear equations in $R^N$”, Adv. Math., 118:2 (1996), 177–243
- G. Diaz, “A note on the Liouville method applied to elliptic eventually degenerate fully nonlinear equations governed by the Pucci operators and the Keller–Osserman condition”, Math. Ann., 353:1 (2012), 145–159
- H. Grosse, A. Martin, Particle physics and the Schrödinger equation, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 6, Cambridge Univ. Press, Cambridge, 1997, xii+167 pp.
- A. Hamydy, M. Massar, N. Tsouli, “Existence of blow-up solutions for a non-linear equation with gradient term in $mathbb R^N$”, J. Math. Anal. Appl., 377:1 (2011), 161–169
- J. Jaroš, K. Takaŝi, “On strongly decreasing solutions of cyclic systems of second-order nonlinear differential equations”, Proc. Roy. Soc. Edinburgh Sect. A, 145:5 (2015), 1007–1028
- J. B. Keller, “On solution of $Delta u=f(u)$”, Comm. Pure Appl. Math., 10:4 (1957), 503–510
- A. A. Kon'kov, “On properties of solutions of quasilinear second-order elliptic inequalities”, Nonlinear Anal., 123/124 (2015), 89–114
- A. V. Lair, “A necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems”, J. Math. Anal. Appl., 365:1 (2010), 103–108
- A. V. Lair, “Entire large solutions to semilinear elliptic systems”, J. Math. Anal. Appl., 382:1 (2011), 324–333
- A. V. Lair, A. Mohammed, “Entire large solutions of semilinear elliptic equations of mixed type”, Commun. Pure Appl. Anal., 8:5 (2009), 1607–1618
- Hong Li, Pei Zhang, Zhijun Zhang, “A remark on the existence of entire positive solutions for a class of semilinear elliptic systems”, J. Math. Anal. Appl., 365:1 (2010), 338–341
- Z. A. Luthey, Piecewise analytical solutions method for the radial Schroedinger equation, Ph.D. thesis, Harvard Univ., Cambridge, 1975 (no paging)
- А. Г. Лосев, Е. А. Мазепа, “Об асимптотическом поведении положительных решений некоторых квазилинейных неравенств на модельных римановых многообразиях”, Уфимск. матем. журн., 5:1 (2013), 83–89
- G. M. Lieberman, “Asymptotic behavior and uniqueness of blow-up solutions of quasilinear elliptic equations”, J. Anal. Math., 115:1 (2011), 213–249
- Е. А. Мазепа, “Положительные решения квазилинейных эллиптических неравенств на модельных римановых многообразиях”, Изв. вузов. Матем., 2015, № 9, 22–30
- A. Mohammed, “Boundary behavior of blow-up solutions to some weighted non-linear differential equations”, Electron. J. Differential Equations, 2002 (2002), 78, 15 pp.
- Y. Naito, H. Usami, “Entire solutions of the inequality $operatorname{div}(A(|Du|)Du)ge f(u)$”, Math. Z., 225:1 (1997), 167–175
- Y. Naito, H. Usami, “Nonexistence results of positive entire solutions for quasilinear elliptic inequalities”, Canad. Math. Bull., 40:2 (1997), 244–253
- R. Osserman, “On the inequality $Delta uge f(u)$”, Pacific J. Math., 7:4 (1957), 1641–1647
- C. L. Pripoae, “Non-holonomic economical systems”, Conference “Applied differential geometry: general relativity”–Workshop “Global analysis, differential geometry, Lie algebras”, BSG Proc., 10, Geom. Balkan Press, Bucharest, 2004, 142–149
- M. D. Smooke, “Error estimates for piecewise perturbation series solutions of the radial Schrödinger equation”, SIAM J. Numer. Anal., 20:2 (1983), 279–295
- Haitao Yang, “On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^N$”, Commun. Pure Appl. Anal., 4:1 (2005), 187–198
- Zhijun Zhang, Song Zhou, “Existence of entire positive $k$-convex radial solutions to Hessian equations and systems with weights”, Appl. Math. Lett., 50 (2015), 48–55
- Xinguang Zhang, “A necessary and sufficient condition for the existence of large solutions to ‘mixed’ type elliptic systems”, Appl. Math. Lett., 25:12 (2012), 2359–2364
- Zhijun Zhang, “Existence of positive radial solutions for quasilinear elliptic equations and systems”, Electron. J. Differential Equations, 2016 (2016), 50, 9 pp.
- Song Zhou, “Existence of entire radial solutions to a class of quasilinear elliptic equations and systems”, Electron. J. Qual. Theory Differ. Equ., 2016 (2016), 38, 10 pp.
- N. Fukagai, K. Narukawa, “On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems”, Ann. Mat. Pura Appl. (4), 186:3 (2007), 539–564
- М. А. Красносельский, Я. Б. Рутицкий, Выпуклые функции и пространства Орлича, Физматгиз, М., 1958, 271 с.
- J. Soria, Tent spaces based on weighted Lorentz spaces. Carleson measures, Ph.D. thesis, Graduate School of Arts and Sciences, Washington Univ., St. Louis, 1990, 121 pp.