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- W4382765724 abstract "This paper focuses on the existence of positive solutions for the following weakly coupled Schrödinger system with supercritical growth except at the origin:$ begin{equation*} left{ begin{array}{ll} -Delta u_1 = mu_1|u_{1}|^{p(r) - 2}u_1 + beta|u_{2}|^{frac{p(r)}{2}}|u_1|^{frac{p(r)}{2}-2}u_{1}, & xin B_1(0), -Delta u_2 = mu_2|u_{2}|^{p(r) - 2}u_{2} + beta|u_{1}|^{frac{p(r)}{2}}|u_2|^{frac{p(r)}{2}-2}u_{2}, & xin B_1(0), end{array} right. end{equation*} $where $ B_1(0) $ is an unit ball $ {mathbb{R}^N} $ with $ Nge 3 $, $ betainmathbb{R} $ is a coupling constant, $ mu_1,mu_2in {mathbb R} $ are constants, $ p(r) = 2^* + r^{alpha} $ with $ 2^* = frac{2N}{N-2} $. Assuming that $ 0<{alpha}<min{frac{N}{2},N-2} $, we apply concentration-compactness idea to show that the problem has a positive solution provided that $ beta>0 $ if $ Nge 5 $ and $ betain(0,beta_0]cup[beta_1,+infty) $ for some positive constants $ beta_0<beta_1 $ if $ N = 3,4 $." @default.
- W4382765724 created "2023-07-01" @default.
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- W4382765724 date "2023-01-01" @default.
- W4382765724 modified "2023-09-28" @default.
- W4382765724 title "Existence of positive solutions for weakly coupled Schrödinger system with supercritical growth" @default.
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- W4382765724 doi "https://doi.org/10.3934/dcdss.2023096" @default.
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