In this Note we present new multiplicity results for the solutions of nonlinear elliptic problems of the form -Delta u + a(x)u = vertical bar u vertical bar(p-1)u in R-N, u is an element of H-1(R-N) where N >= 2, p > 1, p < N+2/N-2 if N >= 3, a is an element of L-loc(N/2) (R-N), in f(R)(N) a > 0. In particular, we have infinitely many positive solutions when there exists a(infinity) > 0 such that lim(vertical bar x vertical bar ->infinity)a(x) = a(infinity) and lim vertical bar x vertical bar ->infinity[a(x) - a(infinity)]e(eta vertical bar x vertical bar) = +infinity for all(eta) > 0.
Molle, R., Passaseo, D. (2015). Multiplicity of solutions of nonlinear scalar field equations. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 26(1), 75-82 [10.4171/RLM/693].
Multiplicity of solutions of nonlinear scalar field equations
MOLLE, RICCARDO
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2015-01-01
Abstract
In this Note we present new multiplicity results for the solutions of nonlinear elliptic problems of the form -Delta u + a(x)u = vertical bar u vertical bar(p-1)u in R-N, u is an element of H-1(R-N) where N >= 2, p > 1, p < N+2/N-2 if N >= 3, a is an element of L-loc(N/2) (R-N), in f(R)(N) a > 0. In particular, we have infinitely many positive solutions when there exists a(infinity) > 0 such that lim(vertical bar x vertical bar ->infinity)a(x) = a(infinity) and lim vertical bar x vertical bar ->infinity[a(x) - a(infinity)]e(eta vertical bar x vertical bar) = +infinity for all(eta) > 0.| File | Dimensione | Formato | |
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