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.

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

See the expanding block below.

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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