Limit cases in an elliptic problem with a parameter-dependent boundary condition

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In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem -Δpu+a(x)u p-1=-urin Ω, |∇u|p-2∂u/ ∂ν=λup-1on ∂Ω for λ∈ℝ, where r>p-1>0, a∈L∞(Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determi...

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Autor principal: García-Melián, J.
Otros Autores: Rossi, J.D, Sabina De Lis, J.C
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2011
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a García-Melián, J. 
245 1 0 |a Limit cases in an elliptic problem with a parameter-dependent boundary condition 
260 |c 2011 
270 1 0 |m García-Melián, J.; Departamento de Análisis Matemático, Universidad de la Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain; email: jjgarmel@ull.es 
506 |2 openaire  |e Política editorial 
504 |a Anane, A., Simplicité et isolation de la première valeur propre du p-Laplacien avec poids (1987) C. R. Acad. Sci. Paris, 305 (1), pp. 725-728 
504 |a Dancer, E.N., Du, Y., On a free boundary problem arising from population biology (2003) Indiana University Mathematics Journal, 52 (1), pp. 51-67 
504 |a Dancer, E.N., Du, Y., Ma, L., Asymptotic behavior of positive solutions of some elliptic problems (2003) Pacific Journal of Mathematics, 210 (2), pp. 215-228 
504 |a García-Melián, J., Rossi, J.D., Sabina De Lis, J., A bifurcation problem governed by the boundary condition I (2007) Nonlinear Differ. Eq. Appl., 14 (5-6), pp. 499-525 
504 |a García-Melián, J., Rossi, J.D., Sabina De Lis, J., Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions (2009) Comm. Contemp. Math., 11, pp. 585-613 
504 |a García-Melián, J., Rossi, J.D., Sabina De Lis, J., Layer profiles of solutions to elliptic problems under parameterdependent boundary conditions (2010) Zeitschrift Anal. Anwend, 29, pp. 1-17 
504 |a García-Melián, J., Rossi, J.D., Sabina De Lis, J., Large solutions to an anisotropic quasilinear elliptic problem (2010) Ann. Math. Pure Appl., 189, pp. 689-712 
504 |a Gilbarg, D., Trudinger, N.S., (1983) Elliptic Partial Differential Equations of Second Order, , Springer-Verlag, Berlin 
504 |a Ladyzhenskaya, O.A., Ural'tseva, N.N., (1968) Linear and Quasilinear Elliptic Equations, , Academic Press, New York 
504 |a Lieberman, G., Boundary regularity for solutions of degenerate elliptic equations (1988) Nonlinear Anal., 12, pp. 1203-1219 
504 |a Lindqvist, P., On the equation div(|δu|p-2δu) + λ|u| p-2u = 0 (1990) Proc. Amer. Math. Soc., 109, pp. 157-164 
504 |a Martínez, S., Rossi, J.D., Isolation and simplicity for the first eigenvalue of the p-Laplacian with a nonlinear boundary condition (2002) Abstr. Appl. Anal., 7, pp. 287-293 
504 |a Matero, J., Quasilinear elliptic equations with boundary blow-up (1996) Journal d'Analyse Mathematique, 69, pp. 229-247 
504 |a Struwe, M., (2008) Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, , Springer-Verlag, Berlin 
504 |a Vázquez, J.L., A strong maximum principle for some quasilinear elliptic equations (1984) Appl. Math. Optim., 12 (3), pp. 191-202 
520 3 |a In this work we discuss existence, uniqueness and asymptotic profiles of positive solutions to the quasilinear problem -Δpu+a(x)u p-1=-urin Ω, |∇u|p-2∂u/ ∂ν=λup-1on ∂Ω for λ∈ℝ, where r>p-1>0, a∈L∞(Ω). We analyze the existence of solutions in terms of a principal eigenvalue, and determine their asymptotic behavior both when r→p-1 and when r→∞. © 2011 - IOS Press and the authors. All rights reserved.  |l eng 
593 |a Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, (1428), Buenos Aires, Argentina 
593 |a Departamento de Análisis Matemático, Universidad de la Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain 
593 |a Instituto Universitario de Estudios Avanzados en Física Atomica, Molecular y Fotonica, Facultad de Física, Universidad de la Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203 La Laguna, Spain 
593 |a Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain 
690 1 0 |a LINEAR AND NONLINEAR EIGENVALUE PROBLEMS 
690 1 0 |a SUB- AND SUPER-SOLUTIONS 
690 1 0 |a VARIATIONAL METHODS 
690 1 0 |a ASYMPTOTIC BEHAVIORS 
690 1 0 |a ASYMPTOTIC PROFILES 
690 1 0 |a ELLIPTIC PROBLEM 
690 1 0 |a EXISTENCE OF SOLUTIONS 
690 1 0 |a NONLINEAR EIGENVALUE PROBLEM 
690 1 0 |a POSITIVE SOLUTION 
690 1 0 |a PRINCIPAL EIGENVALUES 
690 1 0 |a QUASILINEAR PROBLEMS 
690 1 0 |a SUB- AND SUPER-SOLUTIONS 
690 1 0 |a VARIATIONAL METHODS 
690 1 0 |a EIGENVALUES AND EIGENFUNCTIONS 
700 1 |a Rossi, J.D. 
700 1 |a Sabina De Lis, J.C. 
773 0 |d 2011  |g v. 73  |h pp. 147-168  |k n. 3  |p Asymptotic Anal  |x 09217134  |w (AR-BaUEN)CENRE-3856  |t Asymptotic Analysis 
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