The Dirichlet problem with sublinear nonlinearities

Dependence on Parameters for the Dirichlet Problem with Superlinear Nonlinearities

The nonlinear second order differential equation d dt h(t, x′(t)) + g(t, x(t)) = 0, t ∈ [0, T ] a.e. x′(0) = x′(T ) = 0 with superlinear function g is investigated. Based on dual variational method the existence of solution is proved. Dependence on parameters and approximation method are also presented.

Dirichlet Problems with Asymmetric Nonlinearities

Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball with Jumping Nonlinearities

Let p, 0. Let g: R —> R be a locally Lipschitzian function satisfying the superlinear jumping condition: (i) limu->-ao(g(u)/u) e R, (ii) limu^ 0 , and (iii) limu^oo(w/g(u))Nl2(NG(Ku) ((N 2)/2)u • g(u)) = oo for some k 6 (0,1] where G is the primitive of g . Here we prove that the number of solutions of the boundary va...

A Double Eigenvalue Problem for Schrödinger Equations Involving Sublinear Nonlinearities at Infinity

We present some multiplicity results concerning parameterized Schrödinger type equations which involve nonlinearities with sublinear growth at infinity. Some stability properties of solutions with respect to the parameters are also established in an appropriate Sobolev space.

Dirichlet Duality and the Nonlinear Dirichlet Problem

We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F.Hessu/ D 0 on a smoothly bounded domain  b Rn. In our approach the equation is replaced by a subset F Sym.Rn/ of the symmetric n nmatrices with @F fF D 0g. We establish the existence and uniqueness of continuous solutions under an explicit geometric “F -convexity” assumption on the boundary @. We a...