In this paper we are concerned with the following Neumann problem [image omitted] where epsilon is a small positive parameter, f is an odd superlinear and subcritical nonlinearity, is a bounded C4 domain in N without any symmetry assumption. Denoting by H(P), P , the mean curvature of the boundary, it is known that this problem has positive multiple boundary peak solutions with each peak concentrating at a different critical point of H or with all the peaks approaching a local minimum point of H. In this paper we assume that H has a nondegenerate maximum point P0 and we show that there exists a -peak solution with mixed positive and negative peaks concentrating at P0.
Nodal Clustered Solutions for Some Singularly Perturbed Neumann Problems / Teresa, D'Aprile; Pistoia, Angela. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 35:8(2010), pp. 1355-1401. [10.1080/03605302.2010.490284]
Nodal Clustered Solutions for Some Singularly Perturbed Neumann Problems
PISTOIA, Angela
2010
Abstract
In this paper we are concerned with the following Neumann problem [image omitted] where epsilon is a small positive parameter, f is an odd superlinear and subcritical nonlinearity, is a bounded C4 domain in N without any symmetry assumption. Denoting by H(P), P , the mean curvature of the boundary, it is known that this problem has positive multiple boundary peak solutions with each peak concentrating at a different critical point of H or with all the peaks approaching a local minimum point of H. In this paper we assume that H has a nondegenerate maximum point P0 and we show that there exists a -peak solution with mixed positive and negative peaks concentrating at P0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.