Displaying similar documents to “Bifurcation of nonlinear elliptic system from the first eigenvalue.”

Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues

Wolfgang Rother (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove existence and bifurcation results for a semilinear eigenvalue problem in N ( N 2 ) , where the linearization — has no eigenvalues. In particular, we show that under rather weak assumptions on the coefficients λ = 0 is a bifurcation point for this problem in H 1 , H 2 and L p ( 2 p ) .

Existence and bifurcation results for a class of nonlinear boundary value problems in ( 0 , )

Wolfgang Rother (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We consider the nonlinear Dirichlet problem - u ' ' - r ( x ) | u | σ u = λ u in ( 0 , ) , u ( 0 ) = 0 and lim x u ( x ) = 0 , and develop conditions for the function r such that the considered problem has a positive classical solution. Moreover, we present some results showing that λ = 0 is a bifurcation point in W 1 , 2 ( 0 , ) and in L p ( 0 , ) ( 2 p ) .