We study the existence of sign-changing multiple interior spike solutions for the following Dirichlet problem epsilon 2 Delta v - v + f(v) = 0 in Omega, v = 0 on partial derivative Omega, where Omega is a smooth and bounded domain of R-N, epsilon is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity. In particular we prove that if Omega has a plane of symmetry and its intersection with the plane is a two- dimensional strictly convex domain, then, provided that k is even and sufficiently large, a k- peak solution exists with alternate sign peaks aligned along a closed curve near a geodesic of partial derivative Omega.

SOLUTIONS WITH MULTIPLE ALTERNATE SIGN PEAKS ALONG A BOUNDARY GEODESIC TO A SEMILINEAR DIRICHLET PROBLEM / Teresa, D'Aprile; Pistoia, Angela. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 16:1(2014), p. 1350020. [10.1142/s021919971350020x]

SOLUTIONS WITH MULTIPLE ALTERNATE SIGN PEAKS ALONG A BOUNDARY GEODESIC TO A SEMILINEAR DIRICHLET PROBLEM

PISTOIA, Angela
2014

Abstract

We study the existence of sign-changing multiple interior spike solutions for the following Dirichlet problem epsilon 2 Delta v - v + f(v) = 0 in Omega, v = 0 on partial derivative Omega, where Omega is a smooth and bounded domain of R-N, epsilon is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity. In particular we prove that if Omega has a plane of symmetry and its intersection with the plane is a two- dimensional strictly convex domain, then, provided that k is even and sufficiently large, a k- peak solution exists with alternate sign peaks aligned along a closed curve near a geodesic of partial derivative Omega.
multiple interior peaks; 35j20; sign-changing solutions; finite-dimensional reduction 35b40; 35j57; finite-dimensional reduction
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SOLUTIONS WITH MULTIPLE ALTERNATE SIGN PEAKS ALONG A BOUNDARY GEODESIC TO A SEMILINEAR DIRICHLET PROBLEM / Teresa, D'Aprile; Pistoia, Angela. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 16:1(2014), p. 1350020. [10.1142/s021919971350020x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/514027
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