Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory

Calculus of Variations and Partial Differential Equations

Volumn 11, Issue 2, 2000, Pages 143-175

  Grossi, Massimo ^a   Pistoia, Angela ^a   Wei, Juncheng ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003226251     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009907     Document Type: Article

References (30)

1. A. Bahri, Critical point at infinity in some variational problems, Pitman Research Notes Math. 182 Longman House, Harlow (1989),
2. A. Bahri, Y.Y. Li, O. Rey, On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calculus of Variat. 3 (1995), 67-93
3. H. Berestycki, P.L. Lions, Nonlinear scalar field equations I: existence of a ground state, Arch. Rat. Mech. Anal., 82 (1983), 313-346.
4. G. Cerami, J. Wei, Multplicity of multiple interior peaks solutions for some singularly perturbed Neumann problems, Intern. Math. Res. Notes 12 (1998), 601-626.
5. K.C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129 .
6. F.H. Clarke, Optimization and nonsmooth analysis, John Wiley and Sons (1983).
7. E.N. Dancer, S. Yan, Multipeak solutions for a singularly perturbed Neumann problem, Pacific Journal Math.(to appear)
8. A. Floer, A. Weinstein, Nonspreading wave packets for the cubic Scröedinger equation with a bounded potential J. Funct. Anal., 69 (1986), 397-408.
9. N, Mathematical analysis and applications, Part A, Adv. Math. Suppl. Studies, 7A, Acad. Press, New York, 1981.
10. M. Grossi, A. Pistoia, On the effect of critical points of distance function in superlinear elliptic problems, to appear on Advances in Diff. Equat. (1998).
11. C. Gui, Multipeak solutions for a semilinear Neumann problem, Duke Math. J., 84 (1996), 739-769.
12. C. Gui, J. Wei, Multiple interior peak solutions for a for some singularly perturbed Neumann problem, Journ. Diff. Equat. (to appear).
13. C. Gui, J. Wei, M. Winter, Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H.Poincarè (to appear)
14. n , Arch. Rat. Mech. Anal., 105 (1989), 243-266.
15. Y.Y. Li, On a singularly perturbed equation with Neumann boundary condition, Comm. P.D.E. 23 (1998), 487-545.
16. C. Lin, W.M. Ni, I. Takagi, Large amplitude stationary solutions to a chemotaxis system, J. Diff. Eqns., 72 (1988), 1-27.
17. A. Marino, A.M. Micheletti, A. Pistoia, Some variational results on semilinearproblems with asymptotically nonsimmetric behaviour, Nonlinear Analysis "A Tribute in honor of G. Prodi, S.N.S. Pisa (1991), 243-256.
18. W.M. Ni, I. Takagi, On the shape of least energy solutions to a semilinear neumann problem, Comm. Pure Math. Appl., 41 (1991), 819-851.
19. W.M. Ni, I. Takagi, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. Journ., 70 (1992), 247-281.
20. W.M. Ni, J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Math. Appl., 48 (1995), 731-768.
21. A. Pistoia, On the existence of symmetric solutions to some singularly perturbed semi-linear elliptic problems, Asymp. Anal. (to appear).
22. M. Ramos, Teoremas de enlace na teoria dos pontos criticos, Textos de Matematica, Dep. Matematica, Univ. de Lisboa, (1993).
23. S. Yan, On the number of interior multipeak solutions for singularly perturbed Neumann problems, (preprint).
24. Z.Q. Wang, On the existence of multiple single-peaked solution for a semilinear Neumann problem, Arch. Rat. Mech. Anal., 120 (1992), 375-399.
25. J. Wei, On the boundary spike layer solutions to a singularly perturbed Neumann problem, J. Diff. Equat., 134 (1997), 104-133.
26. J. Wei, On the interior spike solutions for some singular perturbation problems Proc. Roy. Soc. Edinb., 128 (1998), 849-874.
27. J. Wei, On the construction of interior spike layer solutions to a singularly perturbed semilinear Neumann problem, Tohoku Math. J., 50 (1998), 159-178.
28. J. Wei, On the construction of interior spike layer solutions to a singularly perturbed semilinear Neumann problem, Partial Differential Equations: Theory and Numerical solution, CRC Press, (1998), 336-349.
29. J. Wei, Conditions for two-peaked solutions of a singularly perturbed elliptic equation, Manuscript. Math. 96 (1998), 113-131.
30. J. Wei, M. Winter, Multiple boundary spike solutions for a wide class of singular perturbation problems J. London Math. Soc., 59 (1999), 82-101.