An exterior nonlinear elliptic problem with a dynamical boundary condition

被引：6

作者：

Fila, Marek ^{[1
]}

Ishige, Kazuhiro ^{[2
]}

Kawakami, Tatsuki ^{[3
]}

机构：

[1] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia

[2] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

[3] Osaka Prefecture Univ, Dept Math Sci, Sakai, Osaka 5998531, Japan

来源：

REVISTA MATEMATICA COMPLUTENSE | 2017年 / 30卷 / 02期

基金：

日本学术振兴会;

关键词：

Semilinear elliptic equation; Exterior domain; Dynamical boundary condition; LAPLACE EQUATION; EXISTENCE; BEHAVIOR; SYSTEMS;

D O I：

10.1007/s13163-017-0225-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Several results on existence, nonexistence and large-time behavior of small positive solutions were obtained before for the equation , , , with a linear dynamical boundary condition. Here is the N-dimensional Laplacian (in x). We study the effects of the change of the domain from the half-space to the exterior of the unit ball when . We show that the critical exponent for the existence of positive solutions and the decay rate of small solutions are different. More precisely, for the half-space problem the critical exponent is and the decay rate is , while for the exterior problem we obtain the exponent and the exponential rate e(-(N-2)t)..

引用

页码：281 / 312

页数：32

共 50 条

[1] An exterior nonlinear elliptic problem with a dynamical boundary condition
Marek Fila
Kazuhiro Ishige
Tatsuki Kawakami
Revista Matemática Complutense, 2017, 30 : 281 - 312
[2] Multiple solutions of a quasilinear elliptic problem involving nonlinear boundary condition on exterior domain
Chen, Caisheng
Zhang, Qi
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2012, 35 (07) : 782 - 794
[3] The Phragmen-Lindelof Theorem for a Fully Nonlinear Elliptic Problem with a Dynamical Boundary Condition
Ishige, Kazuhiro
Nakagawa, Kazushige
GEOMETRIC PROPERTIES FOR PARABOLIC AND ELLIPTIC PDE'S, 2016, 176 : 159 - 171
[4] On a concave–convex elliptic problem with a nonlinear boundary condition
Humberto Ramos Quoirin
Kenichiro Umezu
Annali di Matematica Pura ed Applicata (1923 -), 2016, 195 : 1833 - 1863
[5] Homogenization of nonlinear hyperbolic problem with a dynamical boundary condition
Mohammed, Mogtaba
AIMS MATHEMATICS, 2023, 8 (05): : 12093 - 12108
[6] A nonlinear elliptic eigenvalue–transmission problem with Neumann boundary condition
Luminiţa Barbu
Gheorghe Moroşanu
Cornel Pintea
Annali di Matematica Pura ed Applicata (1923 -), 2019, 198 : 821 - 836
[7] The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition
Zhang, Jinguo
Liu, Xiaochun
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 400 (01) : 100 - 119
[8] On a quasilinear elliptic problem with convection term and nonlinear boundary condition
Marano, Salvatore A.
Winkert, Patrick
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 187 : 159 - 169
[9] On a concave-convex elliptic problem with a nonlinear boundary condition
Ramos Quoirin, Humberto
Umezu, Kenichiro
ANNALI DI MATEMATICA PURA ED APPLICATA, 2016, 195 (06) : 1833 - 1863
[10] A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions
Andreu, F.
Mazon, J. M.
Toledo, J.
Igbida, N.
INTERFACES AND FREE BOUNDARIES, 2006, 8 (04) : 447 - 479

← 1 2 3 4 5 →