Illinois Journal of Mathematics

Solution to biharmonic equation with vanishing potential

Waldemar D. Bastos, Olimpio H. Miyagaki, and Rônei S. Vieira

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Abstract

We establish a result on the existence of nontrivial solution for the following class of biharmonic elliptic equation

\[(\mathrm{P})\quad \Bigl\{\begin{array}{l@{\quad}l}\Delta^{2}u+V(x)u=K(x)f(u)&\mbox{in }R^{N},\\u\neq0,&\mbox{in }R^{N},u\in\mathcal{D}^{2,2}(R^{N}),\end{array}\]

where $\Delta^{2}u=\Delta(\Delta u)$, $V$ and $K$ are nonnegative potentials. $K$ vanishes at infinity and $f$ has a subcritical growth at infinity. The technique used here is the variational approach.

Article information

Source
Illinois J. Math., Volume 57, Number 3 (2013), 839-854.

Dates
First available in Project Euclid: 3 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1415023513

Digital Object Identifier
doi:10.1215/ijm/1415023513

Mathematical Reviews number (MathSciNet)
MR3275741

Zentralblatt MATH identifier
1311.35096

Subjects
Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 35J75: Singular elliptic equations

Citation

Bastos, Waldemar D.; Miyagaki, Olimpio H.; Vieira, Rônei S. Solution to biharmonic equation with vanishing potential. Illinois J. Math. 57 (2013), no. 3, 839--854. doi:10.1215/ijm/1415023513. https://projecteuclid.org/euclid.ijm/1415023513


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