# On some nonlinear hyperbolic p(x,t)-Laplacian equations

On some nonlinear hyperbolic p(x,t)-Laplacian equations AbstractThis paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equationut⁢t=L⁢u+f⁢(x,t) in ⁢ΩT=Ω×(0,T),u_{tt}=Lu+f(x,t)\quad\text{in }\Omega_{T}=\Omega\times(0,T),where L is a nonlinear operator and ϕ⁢(x,t,⋅){\phi(x,t,\cdot\,)}, f⁢(x,t){f(x,t)}and the exponents of the nonlinearities p⁢(x,t){p(x,t)}and μ⁢(x,t){\mu(x,t)}are given functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Analysis de Gruyter

# On some nonlinear hyperbolic p(x,t)-Laplacian equations

, Volume 24 (1): 15 – Jun 1, 2018
15 pages

/lp/degruyter/on-some-nonlinear-hyperbolic-p-x-t-laplacian-equations-2tnIzugUAJ
Publisher
De Gruyter
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6082
eISSN
1869-6082
D.O.I.
10.1515/jaa-2018-0006
Publisher site
See Article on Publisher Site

### Abstract

AbstractThis paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equationut⁢t=L⁢u+f⁢(x,t) in ⁢ΩT=Ω×(0,T),u_{tt}=Lu+f(x,t)\quad\text{in }\Omega_{T}=\Omega\times(0,T),where L is a nonlinear operator and ϕ⁢(x,t,⋅){\phi(x,t,\cdot\,)}, f⁢(x,t){f(x,t)}and the exponents of the nonlinearities p⁢(x,t){p(x,t)}and μ⁢(x,t){\mu(x,t)}are given functions.

### Journal

Journal of Applied Analysisde Gruyter

Published: Jun 1, 2018

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