Radial Nonlinear Elliptic Problems with Singular or Vanishing Potentials

被引：6
作者：
Badiale, Marino [1 ]
Zaccagni, Federica [1 ]
机构：
[1] Univ Turin, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy
来源：
ADVANCED NONLINEAR STUDIES | 2018年 / 18卷 / 02期
关键词：
Nonlinear Elliptic Equations; Weighted Sobolev Spaces; Compact Embeddings; Unbounded or Decaying Potentials; SCHRODINGER-EQUATIONS; SYMMETRIC-SOLUTIONS; EXISTENCE; MULTIPLICITY; COMPACTNESS;
D O I：
10.1515/ans-2018-0007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the existence of radial solutions for the nonlinear elliptic problem -div(A(vertical bar x vertical bar)del u) + V(vertical bar x vertical bar) u = K(vertical bar x vertical bar) f(u) in R-N, with suitable hypotheses on the radial potentials A, V, K. We first get compact embeddings of radial weighted Sobolev spaces into sums of weighted Lebesgue spaces, and then we apply standard variational techniques to get existence results.
引用
收藏
页码：409 / 428
页数：20
相关论文
共 23 条
  • [1] Existence of solutions for a class of nonlinear Schrodinger equations with potential vanishing at infinity
    Alves, Claudianor O.
    Souto, Marco A. S.
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (04) : 1977 - 1991
  • [2] Ambrosetti A, 2005, J EUR MATH SOC, V7, P117
  • [3] Badiale M., 2007, Adv. Differ. Equ, V12, P1321
  • [4] Badiale M, 2006, REND LINCEI-MAT APPL, V17, P1
  • [5] Elliptic problems with singular potential and double-power nonlinearity
    Badiale, Marino
    Rolando, Sergio
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2005, 2 (04) : 417 - 436
  • [6] Compactness and existence results for the p-Laplace equation
    Badiale, Marino
    Guida, Michela
    Rolando, Sergio
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 451 (01) : 345 - 370
  • [7] Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: existence
    Badiale, Marino
    Guida, Michela
    Rolando, Sergio
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (06):
  • [8] Compactness and existence results in weighted Sobolev spaces of radial functions. Part I: compactness
    Badiale, Marino
    Guida, Michela
    Rolando, Sergio
    [J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (01) : 1061 - 1090
  • [9] A nonexistence result for a nonlinear elliptic equation with singular and decaying potential
    Badiale, Marino
    Guida, Michela
    Rolando, Sergio
    [J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2015, 17 (04)
  • [10] Sum of weighted Lebesgue spaces and nonlinear elliptic equations
    Badiale, Marino
    Pisani, Lorenzo
    Rolando, Sergio
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2011, 18 (04): : 369 - 405
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