On Neumann boundary value problems for elliptic equations

Dimitrios A. Kandilakis

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2004)

  • Volume: 24, Issue: 1, page 31-40
  • ISSN: 1509-9407

Abstract

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We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ N , a is a weight function and f a nonlinear perturbation. Our approach is variational in character.

How to cite

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Dimitrios A. Kandilakis. "On Neumann boundary value problems for elliptic equations." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 24.1 (2004): 31-40. <http://eudml.org/doc/271551>.

@article{DimitriosA2004,
abstract = {We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in $ℝ^N$, a is a weight function and f a nonlinear perturbation. Our approach is variational in character.},
author = {Dimitrios A. Kandilakis},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {variational methods; Palais-Smale condition; saddle point theorem; mountain pass theorem; elliptic equation; existence; variational method},
language = {eng},
number = {1},
pages = {31-40},
title = {On Neumann boundary value problems for elliptic equations},
url = {http://eudml.org/doc/271551},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Dimitrios A. Kandilakis
TI - On Neumann boundary value problems for elliptic equations
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2004
VL - 24
IS - 1
SP - 31
EP - 40
AB - We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in $ℝ^N$, a is a weight function and f a nonlinear perturbation. Our approach is variational in character.
LA - eng
KW - variational methods; Palais-Smale condition; saddle point theorem; mountain pass theorem; elliptic equation; existence; variational method
UR - http://eudml.org/doc/271551
ER -

References

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  1. [1] D. Arcoya and L. Orsina, Landesman-Laser conditions and quasilinear elliptic equations, Nonlin. Anal. TMA 28 (1997), 1623-1632. Zbl0871.35037
  2. [2] J. Bouchala and P. Drabek, Strong resonance for some quasilinear elliptic equations, J. Math. Anal. Appl. 245 (2000), 7-19. Zbl0970.35062
  3. [3] P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, NoDEA 7 (2000), 187-199. Zbl0960.35039
  4. [4] F. Cîrstea, D. Motreanu and V. Radulescu, Weak solutions of quasilinear problems with nonlinear boundary condition, Nonlin. Anal. 43 (2001), 623-636. Zbl0972.35038
  5. [5] P. Drabek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singulaties, W. De Gruyter 1997. Zbl0894.35002
  6. [6] W. Li and H. Zhen, The applications of sums of ranges of accretive operators to nonlinear equations involving the p-Laplacian operator, Nonlin. Anal. TMA 24 (2) (1995), 185-193. Zbl0828.35041
  7. [7] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc. Prividence, 1976. 

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