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Resonant anisotropic ▫$(p,q)$▫-equations [Elektronski vir]Gasiński, Leszek ; Papageorgiou, Nikolaos, 1958-We consider an anisotropic Dirichlet problem which is driven by the ▫$(p(z),q(z))$▫-Laplacian (that is, the sum of a ▫$p(z)$▫-Laplacian and a ▫$q(z)$▫-Laplacian). The reaction (source) term, is a ... Carathéodory function which asymptotically as ▫$x \pm\infty$▫ can be resonant with respect to the principal eigenvalue of ▫$(-\Delta_{p(z)}, W^{1,p(z)}_0(\Omega))$▫. First using truncation techniques and the direct method of the calculus of variations, we produce two smooth solutions of constant sign. In fact we show that there exist a smallest positive solution and a biggest negative solution. Then by combining variational tools, with suitable truncation techniques and the theory of critical groups, we show the existence of a nodal (sign changing) solution, located between the two extremal ones.Source: Mathematics [Elektronski vir]. - ISSN 2227-7390 (Vol. 8, iss. 8, Aug. 2020, art. 1332 (21 str.))Type of material - e-article ; adult, seriousPublish date - 2020Language - englishCOBISS.SI-ID - 24916227
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Gasiński, Leszek | ![]() |
Papageorgiou, Nikolaos, 1958- | 38771 |
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