Advanced Search
Article Contents
Article Contents

Invariant criteria for existence of bounded positive solutions

Abstract Related Papers Cited by
  • We consider semilinear elliptic equations $\Delta u \pm \rho(x)f(u) = 0$, or more generally $\Delta u + \varphi(x, u) = 0$, posed in $\R^N$ ($N\geq 3$). We prove that the existence of entire bounded positive solutions is closely related to the existence of bounded solution for $\Delta u + \rho(x) = 0$ in $\mathbb R^N$. Many sufficient conditions which are invariant under the isometry group of $\mathbb R^N$ are established. Our proofs use the standard barrier method, but our results extend many earlier works in this direction. Our ideas can also be applied for the existence of large solutions, for the exterior domain problem and for the system situations.
    Mathematics Subject Classification: 35J60, 35B05, 35B50, 35B35.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(182) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint