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We obtain existence results for some strongly nonlinear Cauchy problems posed in $$ {\mathbb{R}^{N} } $$ and having merely locally integrable data. The equations we deal with have as principal part a bounded, coercive and pseudomonotone operator of Leray-Lions type acting on $$ L^{P} {\left( {0,\,T;\,W^{{1,p}}_{{{\text{loc}}}} {\left( {\mathbb{R}^{N} } \right)}} \right)} $$ , they contain absorbing zero order terms and possibly include first order terms with natural growth. For any p > 1 and under optimal growth conditions on the zero order terms, we derive suitable local a-priori estimates and consequent global existence results.
Journal of Evolution Equations – Springer Journals
Published: Feb 1, 2006
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