2012
DOI: 10.1216/rmj-2012-42-5-1675
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Existence of positive solutions for the $p(x)$-Laplacian equation

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Cited by 5 publications
(9 citation statements)
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“…Up to now, a large number of results have been obtained for solutions to equations related to this operator. For instance, we must mention the works of Kefi-Radulescu [9], Saoudi [10], Kefi-Saoudi [11], Xie-Chen [12], Nhan-Chuong-Truong [13], Zhang [14], Zhang-Motreanu [15], Yucedag [16], Yin-Li-Ke [17], Ait Hammou-Azroul-Lahmi [18], Ayazoglu-Ekincioglu [19], Ge-Wang [20], Ge-Lv [21], Ge-Radulescu [22], Heidarkhani-Afrouzi-Moradi-Caristi-Ge [23], Ge-Zhou-Wu [24], Fan [25] and the references therein. In relation to the regularity for solutions of differential equations with p(x)-Laplacian operator, we refer the readers to to [26][27][28][29][30][31][32][33][34][35][36], respectively, and the references therein.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
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“…Up to now, a large number of results have been obtained for solutions to equations related to this operator. For instance, we must mention the works of Kefi-Radulescu [9], Saoudi [10], Kefi-Saoudi [11], Xie-Chen [12], Nhan-Chuong-Truong [13], Zhang [14], Zhang-Motreanu [15], Yucedag [16], Yin-Li-Ke [17], Ait Hammou-Azroul-Lahmi [18], Ayazoglu-Ekincioglu [19], Ge-Wang [20], Ge-Lv [21], Ge-Radulescu [22], Heidarkhani-Afrouzi-Moradi-Caristi-Ge [23], Ge-Zhou-Wu [24], Fan [25] and the references therein. In relation to the regularity for solutions of differential equations with p(x)-Laplacian operator, we refer the readers to to [26][27][28][29][30][31][32][33][34][35][36], respectively, and the references therein.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…Since the nonlinearity f depends on the gradient ∇u, problem (1) does not have a variational structure, so the variational methods cannot be applied directly. In order to overcome this difficulty, Yin, Li and Ke in [17], by using Krasnoselskii's fixed point theorem on the cone, proved the existence of positive solutions for problem (1) under certain assumptions. Very recently, the authors in [18] used the topological degree theory for a class of demicontinuous operators of generalized (S + ) type to prove the existence of at least one weak solution for problem (1) under the following assumption on f (x, t, ξ):…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
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“…Motivated from the above mentioned papers, especially [12,13], we consider problem (P). Further, as far as we know, there is only one paper which deals with an elliptic equation with variable exponent with dependence on the gradient of the solutions [25], and the present paper is the second.…”
Section: Figueiredo Applied This Methods To a Quasilinear Elliptic Promentioning
confidence: 94%
“…Problems with variable exponent growth conditions also appear in the modelling of stationary thermo-rheological viscous flows of non-Newtonian fluids and in the mathematical description of the processes filtration of an ideal barotropic gas through a porous medium. The detailed application backgrounds of the p(x)-Laplacian can be found in [3,6,22,25] and references therein.…”
Section: Figueiredo Applied This Methods To a Quasilinear Elliptic Promentioning
confidence: 99%