On the bifurcation of the null solutions of some boundary value problems

Abstract

Existence and aymptotic expansion of some bifurcated solution for the following boundary value problem:

\begin{align*} -\Delta u+cu^{2}-B^{2}u & =0,\ \ \ \ \ \ \ x\in \Omega \\ u & =0,\ \ \ \ \ \ \ \partial x\in \Omega \end{align*}

are provided via the Lyapunov-Schmidt method and contraction mapping theorem. The bifurcation point occurs at the first eigenvalue of \(-\Delta\) operator.

Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

nonlinear elliptic BVP; bifurcation point; Lyapunov-Schmidt method; contractions; asymptotic expansion

References

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Paper coordinates

C.I. Gheorghiu, Al. Tămăşan, On the bifurcation of the null solution of some mildly nonlinear elliptic boundary value problems, An. St. Univ. Ovidius Constanta, Seria Matematica, 5 (1996), 59-64.

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Print ISSN

1224-1784

Online ISSN

1844-0835

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