Semilinear elliptic equations with critical nonlinearities

Semilinear Elliptic Equations with Generalized Cubic Nonlinearities

A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.

Oscillation Theory for Semilinear Elliptic Equations with Arbitrary Nonlinearities

Lower order perturbations of critical growth nonlinearities in semilinear elliptic equations

The solvability of semilinear elliptic equations with nonlinearities in the critical growth range depends on the terms with lower order growth. We generalize some known results to a wide class of lower order terms and prove a multiplicity result in the left neighborhood of every eigenvalue of ? when the subcritical term is linear. The proofs are based on variational methods; to assure that the ...

Quasi-concavity for Semilinear Elliptic Equations with Non-monotone and Anisotropic Nonlinearities

An interesting field of modern mathematical research is the study of geometric properties of solutions to elliptic problems. Remarkably, this is often done without any explicit representation of the solution. This paper concentrates on the problem of convexity of level sets for solutions to some elliptic semilinear boundary-value problems in convex rings.More precisely, letΩ0,Ω1 be convex, boun...

A remark on the uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities

We consider the uniqueness of positive solutions to