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ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION
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 Title & Authors
ON A NEUMANN PROBLEM AT RESONANCE FOR NONUNIFORMLY SEMILINEAR ELLIPTIC SYSTEMS IN AN UNBOUNDED DOMAIN WITH NONLINEAR BOUNDARY CONDITION
Hoang, Quoc Toan; Bui, Quoc Hung;
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 Abstract
We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.
 Keywords
semilinear elliptic equation;non-uniform;Landesman-Lazer condition;minimum principle;
 Language
English
 Cited by
1.
On existence of weak solutions for a p-Laplacian system at resonance, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2016, 110, 1, 33  crossref(new windwow)
 References
1.
A. Anane and J. P Gossez, Strongly nonlinear elliptic problems near resonance a variational approach, Comm. Partial Differential Equation 15 (1990), no. 8, 1141-1159. crossref(new window)

2.
D. Arcoya and L. Orsina, Landesman-Lazer condition and quasilinear elliptic equations, Nonlinear Anal. 28 (1997), no. 10, 1623-1632. crossref(new window)

3.
L. Boccando, P. Drabek, and M. Kucera, Landesman-Lazer conditions for strongly non-linear boundary value problems, Comment. Math. Univ. Carolin. 30 (1989), no. 3, 411-427.

4.
N. T. Chung and H. Q. Toan, Existence result for nonuniformly degenerate semilinear elliptic systems in ${\mathbb{R}}^N$, Glasgow Math. J. 51 (2009), 561-570. crossref(new window)

5.
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag Berlin, 2001.

6.
T. T. M. Hang and H. Q. Toan, On existence of weak solutions of Neumann problem for quasilinear elliptic equations involving p-Laplacian in an unbounded domain, Bull. Korean Math. Soc 48 (2011), no. 6, 1169-1182. crossref(new window)

7.
D. A. Kandilakis and M. Magiropoulos, A p-Laplacian system with resonance and non-linear boundary conditions on an unbounded domain, Comment. Math. Univ. Carolin. 48 (2007), no. 1, 59-68.

8.
N. Lam and G. Lu, Existence and multiplicity of solutions to equations of N-Laplacian type with critical exponential growth in ${\mathbb{R}}^N$, J. Funct. Anal. 262 (2012), no. 3, 1132-1165. crossref(new window)

9.
M. Lucia, P. Magrone, and Huan-Songzhou, A Dirichlet problem with asymptotically linear and changing sign nonlinearity, Rev. Mat. Complut. 16 (2003), no. 2, 465-481.

10.
Q. A. Ngo and H. Q. Toan, Existence of solutions for a resonant problem under Landesman-Lazer condition, Electron. J. Differential Equations 2008 (2008), no. 98, 1-10.

11.
Q. A. Ngo and H. Q. Toan, Some remarks on a class of nonuniformly elliptic equations of p-Laplacian type, Acta Appl. Math. 106 (2009), no. 2, 229-239. crossref(new window)

12.
M. Struwe, Variational Methods, Second edition, Springer Verlag, 2008.

13.
H. Q. Toan and N. T. Chung, Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains, Nonlinear Anal. 70 (2009), no. 11, 3987-3996. crossref(new window)

14.
P. Tomiczek, A generalization of the Landesman-Lazer condition, Electron. J. Differential Equations 2001 (2001), no. 4, 1-11.

15.
Z.-Q. Ou and C.-L. Tang, Resonance problems for the p-Laplacian systems, J. Math. Anal. Appl. 345 (2008), no. 1, 511-521. crossref(new window)

16.
N. B. Zographopoulos, p-Laplacian systems on resonance, Appl. Anal. 83 (2004), no. 5, 509-519. crossref(new window)