<p style='text-indent:20px;'>This paper deals with stability of solution map to a parametric control problem governed by semilinear elliptic equations finite unilateral constraints, where the objective functional is not convex. By using first-order necessary optimality conditions, we derive some sufficient conditions under which upper semicontinuous respect parameters.</p>

In this note, we prove a blow-up result for the semilinear damped wave equation in compact Lie group with power nonlinearity $|u|^p$ any $p>1$, under suitable integral sign assumptions initial data, by using an iteration argument. A byproduct of method is upper bound estimate lifespan local time solution. As preliminary result, (in time) existence proved energy space via Fourier analysis on gro...

We want to explain the crucial difference between the second order (m = 1) and higher order (m > 1) case. If m = 1 a very satisfactory result is known. Indeed, the sign condition (2) alone is sufficient to ensure classical solvability of the Dirichlet problem (1). There are two very strong devices in the theory of second order elliptic equations, which make the proof of the needed a-priori maxi...

Article history: Received 25 October 2007 Available online 29 March 2008 Submitted by P.J. McKenna

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.