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Existence and qualitative properties of solutions for nonlinear Dirichlet problems
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Subharmonic solutions for nonlinear second order equations in presence of lower and upper solutions
Lyapunov inequalities for partial differential equations at radial higher eigenvalues
1. | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva. 18071 Granada, Spain, Spain |
References:
[1] |
A. Cañada, J. A. Montero and S. Villegas, Liapunov-type inequalities and Neumann boundary value problems at resonance, Math. Inequal. Appl., 8 (2005), 459-475. |
[2] |
A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal., 237 (2006), 176-193.
doi: 10.1016/j.jfa.2005.12.011. |
[3] |
A. Cañada and S. Villegas, Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues, J. Eur. Math. Soc. (JEMS), 12 (2010), 163-178. |
[4] |
M. del Pino and R. F. Manásevich, Global bifurcation from the eigenvalues of the p-Laplacian, J. Differential Equations, 92 (1991), 226-251.
doi: 10.1016/0022-0396(91)90048-E. |
[5] |
C. L. Dolph, Nonlinear integral equations of the Hammerstein type, Trans. Amer. Math. Soc., 66 (1949), 289-307.
doi: 10.1090/S0002-9947-1949-0032923-4. |
[6] |
B. Fuglede, Continuous domain dependence of the eigenvalues of the Dirichlet Laplacian and related operators in Hilbert space, J. Funct. Anal., 167 (1999), 183-200.
doi: 10.1006/jfan.1999.3442. |
[7] |
P. Hartman, "Ordinary Differential Equations," John Wiley & Sons, Inc., New York-London-Sydney, 1964. |
[8] |
Y. Li and H. Z. Wang, Neumann boundary value problems for second-order ordinary differential equations across resonance, SIAM J. Control Optim., 33 (1995), 1312-1325.
doi: 10.1137/S036301299324532X. |
[9] |
G. Vidossich, Existence and uniqueness results for boundary value problems from the comparison of eigenvalues, ICTP Preprint Archive, 1979015, (1979). |
[10] |
M. Zhang, Certain classes of potentials for $p$-Laplacian to be non-degenerate, Math. Nachr., 278 (2005), 1823-1836.
doi: 10.1002/mana.200410342. |
show all references
References:
[1] |
A. Cañada, J. A. Montero and S. Villegas, Liapunov-type inequalities and Neumann boundary value problems at resonance, Math. Inequal. Appl., 8 (2005), 459-475. |
[2] |
A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal., 237 (2006), 176-193.
doi: 10.1016/j.jfa.2005.12.011. |
[3] |
A. Cañada and S. Villegas, Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues, J. Eur. Math. Soc. (JEMS), 12 (2010), 163-178. |
[4] |
M. del Pino and R. F. Manásevich, Global bifurcation from the eigenvalues of the p-Laplacian, J. Differential Equations, 92 (1991), 226-251.
doi: 10.1016/0022-0396(91)90048-E. |
[5] |
C. L. Dolph, Nonlinear integral equations of the Hammerstein type, Trans. Amer. Math. Soc., 66 (1949), 289-307.
doi: 10.1090/S0002-9947-1949-0032923-4. |
[6] |
B. Fuglede, Continuous domain dependence of the eigenvalues of the Dirichlet Laplacian and related operators in Hilbert space, J. Funct. Anal., 167 (1999), 183-200.
doi: 10.1006/jfan.1999.3442. |
[7] |
P. Hartman, "Ordinary Differential Equations," John Wiley & Sons, Inc., New York-London-Sydney, 1964. |
[8] |
Y. Li and H. Z. Wang, Neumann boundary value problems for second-order ordinary differential equations across resonance, SIAM J. Control Optim., 33 (1995), 1312-1325.
doi: 10.1137/S036301299324532X. |
[9] |
G. Vidossich, Existence and uniqueness results for boundary value problems from the comparison of eigenvalues, ICTP Preprint Archive, 1979015, (1979). |
[10] |
M. Zhang, Certain classes of potentials for $p$-Laplacian to be non-degenerate, Math. Nachr., 278 (2005), 1823-1836.
doi: 10.1002/mana.200410342. |
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