The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation
We consider the Dirichlet problem Kp p(x) u(x) − ∆ Kq q(x) u(x) = f(x, u(x), ∇u(x)) in Ω, u = 0, driven by the sum of a p(x)-Laplacian operator and of a q(x)-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet, Kirchhoff egyenlet, Dirichlet probléma |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/76540 |
| Tartalmi kivonat: | We consider the Dirichlet problem Kp p(x) u(x) − ∆ Kq q(x) u(x) = f(x, u(x), ∇u(x)) in Ω, u = 0, driven by the sum of a p(x)-Laplacian operator and of a q(x)-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and strong generalized solution, using topological tools (properties of Galerkin basis and of Nemitsky map). In the particular case of a positive Kirchhoff term, we obtain the existence of weak solution (= strong generalized solution), using the properties of pseudomonotone operators. |
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| Terjedelem/Fizikai jellemzők: | 16 |
| ISSN: | 1417-3875 |