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Existence and asymptotic behavior of boundary blow-up solutions for weighted \(p(x)\)-Laplacian equations with exponential nonlinearities. (English) Zbl 1216.35064
This paper investigates the following \(p(x)\)-Laplacian equations with exponential nonlinearities: \(-\Delta_{p(x)}u+ \rho(x) e^{f(x,u)}=0\) in \(\Omega\), \(u(x)\to+\infty\) as \(d(x,\partial\Omega)\to 0\), where \(-\Delta_{p(x)}u= -\text{div}(|\nabla u|^{p(x)-2}\nabla u)\) is called \(p(x)\)-Laplacian, \(\rho(x)\in C(\Omega)\). The asymptotic behavior of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.
MSC:
35J70 Degenerate elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35B44 Blow-up in context of PDEs
35D30 Weak solutions to PDEs
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