Exact multiplicity and numerical computation of solutions for two classes of non-autonomous problems with concave-convex nonlinearities. (English) Zbl 1284.35188
Summary: We establish the exact multiplicity of positive solutions and the global solution structure for two classes of problems on circular domains. The first class involves non-autonomous concave-convex problems on a ball in \(\mathbb R^n\), and the second one deals with concave-convex problems on a “thin” annulus in \(\mathbb R^n\). We illustrate our results by numerical computations, using a novel algorithm, which involves continuation in a global parameter.
MSC:
| 35J61 | Semilinear elliptic equations |
| 65N99 | Numerical methods for partial differential equations, boundary value problems |
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