Multiplicity Results for Nonlinear Nonhomogeneous Robin Problems with Indefinite Potential Term

被引：0
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作者：
Yunru Bai
Nikolaos S. Papageorgiou
Shengda Zeng
机构：
[1] Guangxi University of Science and Technology,School of Science
[2] National Technical University,Department of Mathematics
[3] Yulin Normal University,Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing
[4] Nanjing University,Department of Mathematics
[5] Jagiellonian University in Krakow,Faculty of Mathematics and Computer Science
来源：
Results in Mathematics | 2023年 / 78卷
关键词：
Nonlinear regularity; nonlinear maximum principle; constant sign solutions; nodal solutions; second deformation theorem; critical groups; indefinite potential function; 35J20; 35J60; 58E05;
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摘要：
We consider a nonlinear Robin problem driven by a general nonhomogeneous differential operator plus an indefinite potential term. The reaction is of generalized logistic type. Using variational tools we prove a multiplicity theorem producing three nontrivial solutions with sign information (positive, negative and nodal). In the particular case of (p, 2)-equations, employing also critical groups, we produce a second nodal solution. Our results extend earlier multiplicity results for coercive problems.
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