Multiple solutions for resonant problems of the Robin p-Laplacian plus an indefinite potential

被引：2
|
作者：
Papageorgiou, Nikolaos S. [1 ,2 ]
Radulescu, Vicentiu D. [3 ,4 ]
Repovs, Dusan D. [5 ,6 ]
机构：
[1] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece
[2] King Saud Univ, Dept Math, POB 2454, Riyadh 11451, Saudi Arabia
[3] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia
[4] Univ Craiova, Dept Math, Craiova 200585, Romania
[5] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia
[6] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2017年 / 56卷 / 03期
关键词：
NONLINEAR NEUMANN PROBLEMS; EXISTENCE; EQUATIONS; SIGN;
D O I：
10.1007/s00526-017-1164-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a nonlinear boundary value problem driven by the p-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carathodory function which is asymptotically resonant at +/-infinity with respect to a nonprincipal Ljusternik-Schnirelmann eigenvalue. Using variational methods, together with Morse theory and truncation-perturbation techniques, we show that the problem has at least three nontrivial smooth solutions, two of which have a fixed sign.
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页数：23
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