Geodesic
Variational inequalities with the logistic type nonlinearities and dependence on the gradient
Filomat, Tome 36 (2022) no. 12, p. 4055

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DOI

In this paper, we study the following variational inequality u ∈ K, 〈Au, v − u〉 + ∫ Ω 1(x,u)(v − u) ≥ ∫ Ω f (x,u,∇u)(v − u),∀v ∈ K, where K = {u ∈ W1,p0 (Ω) : u(x) ≥ 0}, A is the p- Laplacian and the function 1 is increasing in the second variable. By constructing the solution operator for an associate variational inequality, we reduce the problem to a fixed point equation. Then, we apply the fixed point index to prove the existence of the nontrivial solution of the problem.
DOI : 10.2298/FIL2212055Q
Classification : 35J60, 47H07, 47H10
Keywords: variational inequalities, fixed point index, logistic type nonlinearity, gradient, positive solutions 
Bui The Quan; Nguyen Bich Huy. Variational inequalities with the logistic type nonlinearities and dependence on the gradient. Filomat, Tome 36 (2022) no. 12, p. 4055 . doi: 10.2298/FIL2212055Q
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     title = {Variational inequalities with the logistic type nonlinearities and dependence on the gradient},
     journal = {Filomat},
     pages = {4055 },
     year = {2022},
     volume = {36},
     number = {12},
     doi = {10.2298/FIL2212055Q},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212055Q/}
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