Asymptotic Behaviour of a Semilinear Elliptic System with a Large Exponent

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

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.

Asymptotic behaviour for a semilinear nonlocal equation

We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...

Local Solvability and Regularity Results for a Class of Semilinear Elliptic Problems in Nonsmooth Domains

We consider a class of semilinear elliptic problems in twoand three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Fréchet differentiable. Applying ...

Existence and Asymptotic Behaviour of Positive Solutions for Semilinear Elliptic Systems in the Euclidean Plane

We study the semilinear elliptic system ∆u = λp(x)f(v),∆v = λq(x)g(u), in an unbounded domain D in R2 with compact boundary subject to some Dirichlet conditions. We give existence results according to the monotonicity of the nonnegative continuous functions f and g. The potentials p and q are nonnegative and required to satisfy some hypotheses related on a Kato class.