Abstract
AbstractIn this paper we study anisotropic weighted (p, q)-equations with a parametric right-hand side depending on the gradient of the solution. Under very general assumptions on the data and by using a topological approach, we prove existence and uniqueness results and study the asymptotic behavior of the solutions when both the $$q(\cdot )$$
q
(
·
)
-Laplacian on the left-hand side and the reaction term are modulated by a parameter. Moreover, we present some properties of the solution sets with respect to the parameters.
Funder
Technische Universität Berlin
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Reference26 articles.
1. Averna, D., Motreanu, D., Tornatore, E.: Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence. Appl. Math. Lett. 61, 102–107 (2016)
2. Bahrouni, A., Rădulescu, V.D., Repovš, D.: Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves. Nonlinearity 32(7), 2481–2495 (2019)
3. Cherfils, L., Il’yasov, Y.: On the stationary solutions of generalized reaction diffusion equations with $$p$$ &$$q$$-Laplacian. Commun. Pure Appl. Anal. 4(1), 9–22 (2005)
4. De Figueiredo, D., Girardi, M., Matzeu, M.: Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques. Differ. Integral Equ. 17(1–2), 119–126 (2004)
5. Diening, L., Harjulehto, P., Hästö, P., et al.: Lebesgue and Sobolev Spaces with Variable Exponents, p. 2011. Springer, Heidelberg (2011)
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献