Title:	On sign-changing solutions for (p, q)-Laplace equations with two parameters
Authors:	Bobkov, Vladimír Mieko, Tanaka
Citation:	BOBKOV, V., MIEKO, T. On sign-changing solutions for (p, q)-Laplace equations with two parameters. Advances in Nonlinear Analysis, 2019, roč. 8, č. 1, s. 101-129. ISSN 2191-9496.
Issue Date:	2019
Publisher:	De Gruyter
Document type:	článek article
URI:	2-s2.0-85062600794 http://hdl.handle.net/11025/33877
ISSN:	2191-9496
Keywords in different language:	(p, q)-Laplacian;p-Laplacian;eigenvalue problem;first eigenvalue;second eigenvalue;nodal solutions;sign-changing solutions;Nehari manifold;linking theorem;descending flow.
Abstract in different language:	We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for a two-parametric family of partially homogeneous (p, q)-Laplace equations −Δpu − Δqu = α|u|p−2u + β|u|q−2u where p ≠ q. By virtue of the Nehari manifolds, the linking theorem, and descending flow, we explicitly characterize subsets of the (α, β)-plane which correspond to the existence of nodal solutions. In each subset the obtained solutions have prescribed signs of energy and, in some cases, exactly two nodal domains. The nonexistence of nodal solutions is also studied. Additionally, we explore several relations between eigenvalues and eigenfunctions of the p- and q-Laplacians in one dimension.
Rights:	© De Gruyter
Appears in Collections:	Články / Articles (KMA) OBD

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