In this paper we consider the quasilinear elliptic problem In this paper we consider the quasilinear elliptic problem $$ $$ -Delta_p u=lambda |x|^{delta} f(u) quad extrm{in }B_1(0)$$ $$ u=0 quad extrm{in }partial B_1(0), $$ where $f$ is nonnegative. We assume $f(0)=0$, that there is $U>0$ such that $f(U)=0$, and that $f$ is subcritical in $0$ and in $U$ with respect to Sobolev. We show that there is a positive $lambda^*$ such that for $lambda>lambda^*$ there are at least three positive radial solutions. The same conclusion is obtained replacing the subcriticality in $U$ with the subcriticality of $f$ for $u$ large. where $f$ is nonnegative. We assume $f(0)=0$, that there is $U>0$ such that $f(U)=0$, and that $f$ is subcritical in $0$ and in $U$ with respect to Sobolev. We show that there is a positive $lambda^*$ such that for $lambda>lambda^*$ there are at least three positive radial solutions. The same conclusion is obtained replacing the subcriticality in $U$ with the subcriticality of $f$ for $u$ large.

Isabel Flores, Matteo Franca, Leonelo Iturriaga (2019). Positive radial solutions involving nonlinearities with zeros. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(5), 2555-2579 [10.3934/dcds.2019107].

Positive radial solutions involving nonlinearities with zeros

Matteo Franca
Membro del Collaboration Group
;
2019

Abstract

In this paper we consider the quasilinear elliptic problem In this paper we consider the quasilinear elliptic problem $$ $$ -Delta_p u=lambda |x|^{delta} f(u) quad extrm{in }B_1(0)$$ $$ u=0 quad extrm{in }partial B_1(0), $$ where $f$ is nonnegative. We assume $f(0)=0$, that there is $U>0$ such that $f(U)=0$, and that $f$ is subcritical in $0$ and in $U$ with respect to Sobolev. We show that there is a positive $lambda^*$ such that for $lambda>lambda^*$ there are at least three positive radial solutions. The same conclusion is obtained replacing the subcriticality in $U$ with the subcriticality of $f$ for $u$ large. where $f$ is nonnegative. We assume $f(0)=0$, that there is $U>0$ such that $f(U)=0$, and that $f$ is subcritical in $0$ and in $U$ with respect to Sobolev. We show that there is a positive $lambda^*$ such that for $lambda>lambda^*$ there are at least three positive radial solutions. The same conclusion is obtained replacing the subcriticality in $U$ with the subcriticality of $f$ for $u$ large.
2019
Isabel Flores, Matteo Franca, Leonelo Iturriaga (2019). Positive radial solutions involving nonlinearities with zeros. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(5), 2555-2579 [10.3934/dcds.2019107].
Isabel Flores; Matteo Franca; Leonelo Iturriaga
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/721078
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