Spike-layered Solutions of Singularly Perturbed Elliptic Problems in a Degenerate Setting

Indiana University Mathematics Journal

Volumn 48, Issue 3, 1999, Pages 883-898

  Del Pino, Manuel ^a   Felmer, Patricio L ^a  

^a DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Elliptic equations; Singular perturbations; Spikes

Indexed keywords

EID: 0001663580     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1999.48.1596     Document Type: Article

References (15)

1. A. AMBROSETTI, M. BADIALE , S. CINGOLANI. Semiclassical states of nonlinear Schrödinger equations To appear in Arch. Rational Mech. Anal. 140 285-300 (1997).
2. M. DEL PINO, P. FELMER. Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Var. and PDE 4, 121-137 (1996).
3. M. DEL PINO, P. FELMER. Multi-peak bound states of nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Anal. Nonlineaire 15, 127-149 (1998).
4. M. DEL PINO, P. FELMER. bound states of nonlinear Schrödinger equations. J. of Functional Analysis 149, 245-265 (1997).
5. M. DEL PINO, P. FELMER AND J. WEI. Multi-peak solutions for some singular perturbation problems To appear in Calculus of Variations and PDE's.
6. W.Y DING, W.M. NI. On the existence of Positive Entire Solutions of a Semilinear Elliptic Equation. Arch. Rat. Mech. Anal., 91, 283-308 (1986).
7. A. FLOER, A. WEINSTEIN. Nonspreading Wave Packets for the Cubic Schrödinger Equation with a Bounded Potential, Journal of Functional Analysis 69, 397-408 (1986).
8. n, Adv. Math. Suppl. Stud. 7A, Math. Anal. Appl. Part A (1981) 369-402.
9. Y. Y. LI. On a Singularly Perturbed Elliptic Equation. Advances in Differential Equations 2, 955-980 (1997).
10. Y. Y. LI. On a Singularly Perturbed Elliptic Equation with Neumann boundary conditions. Comm. in Partial Diff. Equations 23 487-545 (1998).
11. Y. Y. LI, L. NIRENBERG. The Dirichlet problem for singularly perturbed elliptic equations. Comm. Pure Appl. Math. 51 1445-1490 (1998).
12. W. M. NI, I. TAKAGI. On the shape on least-energy solutions to a semilinear Neumann problem. Comm. on Pure and App. Math. Vol. XLIV, 819-851, (1991).
13. W.-M. NI, I. TAKAGI. Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), 247-281.
14. W.-M. NI, J. WEI. On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995), 731-7 68.
15. a. Comm. Partial Diff. Eq. 13, 1499-1519 (1988).