MULTIPLE SOLUTIONS FOR PERTURBED QUASILINEAR ELLIPTIC PROBLEMS

被引：1

作者：

Bartolo, Rossella ^{[1
]}

Candela, Anna Maria ^{[2
]}

Salvatore, Addolorata ^{[2
]}

机构：

[1] Politecnico Bari, Dipartimento Meccan Matemat & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Bari Aldo Moro, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2023年 / 61卷 / 01期

关键词：

(p; q)-quasilinear elliptic equation; asymptotically (q-1)-linear problem; q)-Laplacian operator; variational methods; essential value; perturbed problem; pseudo-genus; quasi-eigenvalue; regularity of solutions; P-LAPLACIAN PROBLEMS; WEAK SOLUTIONS; EQUATIONS; REGULARITY; NONLINEARITY; EXISTENCE;

D O I：

10.12775/TMNA.2022.069

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence of multiple solutions for the (p q)-quasilinear elliptic problem {-Delta(p)u - Delta(q)u = g(x; u) + epsilon h(x, u) in Omega u = 0 on partial derivative Omega where 1 < p < q < +infinity, Omega is an open bounded domain of R-N, the non-linearity g(x, u) behaves at infinity as vertical bar u vertical bar(q-1), epsilon is an element of R and h is an element of C(<(Omega)over bar> x R, R). In spite of the possible lack of a variational structure of this problem, from suitable assumptions on g(x, u) and appropriate procedures and estimates, the existence of multiple solutions can be proved for small perturbations.

引用

页码：549 / 574

页数：26

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