On Neumann boundary value problems for elliptic equations

• Autorzy: Dimitrios A. Kandilakis
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

variational methods; Palais-Smale condition; saddle point theorem; mountain pass theorem

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35J60: Nonlinear elliptic equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 31-40

Daty

wydano

2004

otrzymano

2004-03-07

Twórcy

autor

Dimitrios A. Kandilakis

• Department of Sciences, Technical University of Crete, Chania, Crete 73100, Greece

Bibliografia

• [1] D. Arcoya and L. Orsina, Landesman-Laser conditions and quasilinear elliptic equations, Nonlin. Anal. TMA 28 (1997), 1623-1632.
• [2] J. Bouchala and P. Drabek, Strong resonance for some quasilinear elliptic equations, J. Math. Anal. Appl. 245 (2000), 7-19.
• [3] P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, NoDEA 7 (2000), 187-199.
• [4] F. Cîrstea, D. Motreanu and V. Radulescu, Weak solutions of quasilinear problems with nonlinear boundary condition, Nonlin. Anal. 43 (2001), 623-636.
• [5] P. Drabek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singulaties, W. De Gruyter 1997.
• [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.
• [7] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc. Prividence, 1976.

Identyfikatory

DOI

10.7151/dmgt.1050