Advances in Differential Equations

Nodal solutions to a class of nonstandard superlinear equations on $\Bbb R^N$

Monica Conti, Susanna Terracini, and Gianmaria Verzini

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Abstract

We investigate the existence of sign-changing radial solutions for a class of singular equations: $$ -\Delta u(x)+ b(|x|)u(x) = |u(x)|^{\theta-1}u(x)+h(|x|)\hspace{1cm}x\in\mathbb R^N $$ where $b(|x|)$ may change sign and behaves like $|x|^{-\alpha}$ at infinity for some $\alpha\in(0,2)$, and $\theta>1$.

Article information

Source
Adv. Differential Equations Volume 7, Number 3 (2002), 297-318.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651827

Mathematical Reviews number (MathSciNet)
MR1867689

Zentralblatt MATH identifier
1126.35316

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 34B15: Nonlinear boundary value problems 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Conti, Monica; Terracini, Susanna; Verzini, Gianmaria. Nodal solutions to a class of nonstandard superlinear equations on $\Bbb R^N$. Adv. Differential Equations 7 (2002), no. 3, 297--318. https://projecteuclid.org/euclid.ade/1356651827.


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