Singular Hamiltonian elliptic systems involving double exponential growth in dimension two
In this research, we are interested to investigate the existence of nontrivial weak solutions to the following Hamiltonian elliptic system −div(ω(x)∇u)=g(v)|x|a,x∈B1(0),−div(ω(x)∇v)=f(u)|x|b,x∈B1(0),with Dirichlet boundary conditions, where a,b∈[0,2), the weight ω(x) is of logarithmic type and the n...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124000676 |
| Summary: | In this research, we are interested to investigate the existence of nontrivial weak solutions to the following Hamiltonian elliptic system −div(ω(x)∇u)=g(v)|x|a,x∈B1(0),−div(ω(x)∇v)=f(u)|x|b,x∈B1(0),with Dirichlet boundary conditions, where a,b∈[0,2), the weight ω(x) is of logarithmic type and the nonlinearities f and g possess double exponential growth. To establish the existence of solutions, our approach involves utilizing the linking theorem and a finite-dimensional approximation. |
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| ISSN: | 2666-8181 |