Quasi-concavity for semilinear elliptic equations with non-monotone and anisotropic nonlinearities

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...

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

Forced vibrations of wave equations with non-monotone nonlinearities

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a mi...

Monotone Iterative Technique for Semilinear Elliptic Systems

We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...