Periodic solutions of non-Newtonian polytropic filtration equations with nonlinear sources

The BV solution of the parabolic equation with degeneracy on the boundary

“…Some other related references, one can refer to Refs. [12][13][14][15][16]. The paper is arranged as following.…”

“…Unlike the equation (16), to the best knowledge of the authors, considering the parabolic equation related to the p Laplacian, our paper is the first one to study the stability of the solutions based on a partial boundary condition (4). Of course, whether the condition (12) in Theorem 1.6 and the assumption that u; v are regular in Theorem 1.7 are necessary or not? This is a very interesting problem to be studied in the future.…”

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

“…In 2010, under a convex assumption on the domain Ω, Wang et al 4 considered a partial case of . While, there are no results about the cases of and before the present work.…”

Nontrivial, nonnegative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms

“…[3], [5], [6], [7], [21], [22], [25], [26], [29], [31], [35], [42], [50], [56], [57], [60], [67], [68]. We also recall the related problems faced in [23] and [24] also for higher order operators, and in [19] for p = 2 and N = 1.…”

“…Indeed, this choice enable us to establish the required a priori bounds on the solutions of the approximating problem (2.1) in a uniform way with respect to the perturbation parameter > 0. We remark that, if the diffusion is slow and Ω ⊂ R N is a bounded and open domain, then we can allow a superlinear growth in u, v in order to have both global existence solutions and periodic solutions, together with their L ∞ -estimates, see [8], [13], [14], [45], [48], [49], [57], [60], [61], [62], [63] and the references therein. Due to the singularity of the p, q-Laplacian, the way of proving the a priori bounds deeply differs from that employed in [25] and [26].…”