On the bifurcation of the null solutions of some mildly nonlinear elliptic boundary value problems


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,\ \ \ \ \ \ \ x\in \partial \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.


C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis


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


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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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