Varying bifurcation diagrams of positive solutions for a class of indefinite superlinear boundary value problems. (English) Zbl 0940.35095
Let \(L\) be a uniformly elliptic operator and \(a(x)=a^+(x)-\varepsilon a^-(x)\) be a weight of variable sign. This paper deals with positive solutions of \(Lu=\lambda u -a(x)u^2\) in a bounded domain with homogeneous boundary conditions. This type of problem has a rich structure of solutions depending on the parameters \(\lambda\) and \(\varepsilon\). A fairly complete analysis is given based on bifurcation techniques and on comparison principles. Included is a study of stability of the various solutions.
Reviewer: Catherine Bandle (Basel)
MSC:
35J65 | Nonlinear boundary value problems for linear elliptic equations |
35B32 | Bifurcations in context of PDEs |
35K20 | Initial-boundary value problems for second-order parabolic equations |
35B60 | Continuation and prolongation of solutions to PDEs |
35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |