EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 411-418
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We study a partial differential equation on a bounded domain $\Omega\subset\mathbb{R}^N$ with a $p(x)$-growth condition in the divergence operator and we establish the existence of at least two nontrivial weak solutions in the generalized Sobolev space $W_0^{1,p(x)}(\Omega)$. Such equations have been derived as models of several physical phenomena. Our proofs rely essentially on critical point theory combined with corresponding variational techniques.
MIHĂILESCU, MIHAI. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 411-418. doi: 10.1017/S0017089506003144
@article{10_1017_S0017089506003144,
author = {MIH\u{A}ILESCU, MIHAI},
title = {EXISTENCE {AND} {MULTIPLICITY} {OF} {SOLUTIONS} {FOR} {AN} {ELLIPTIC} {EQUATION} {WITH} $p(x)${-GROWTH} {CONDITIONS}},
journal = {Glasgow mathematical journal},
pages = {411--418},
year = {2006},
volume = {48},
number = {3},
doi = {10.1017/S0017089506003144},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003144/}
}
TY - JOUR AU - MIHĂILESCU, MIHAI TI - EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS JO - Glasgow mathematical journal PY - 2006 SP - 411 EP - 418 VL - 48 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003144/ DO - 10.1017/S0017089506003144 ID - 10_1017_S0017089506003144 ER -
%0 Journal Article %A MIHĂILESCU, MIHAI %T EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR AN ELLIPTIC EQUATION WITH $p(x)$-GROWTH CONDITIONS %J Glasgow mathematical journal %D 2006 %P 411-418 %V 48 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003144/ %R 10.1017/S0017089506003144 %F 10_1017_S0017089506003144
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