Normalized ground states for semilinear elliptic systems with critical and subcritical nonlinearities

Semilinear Elliptic Systems With Exponential Nonlinearities in Two Dimensions ∗

We establish a priori bounds for positive solutions of semilinear elliptic systems of the form 8><>>>: −∆u = g(x, v) , in Ω −∆v = f(x, u) , in Ω u > 0 , v > 0 in Ω

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

Critical and Subcritical Elliptic Systems in dimension two

In this paper we study the existence of nontrivial solutions for the following system of two coupled semilinear Poisson equations: (S) 8 < : ?u = g(v); v > 0 in ; ?v = f (u); u > 0 in ; u = 0; v = 0 on @ ; where is a bounded domain in R 2 with smooth boundary @ , and the functions f and g have the maximal growth which allow us to treat problem (S) variationally in the Sobolev space H 1 0 ((). W...

Existence result for semilinear elliptic systems involving critical exponents

where ⊂RN (N ≥ ) is a smooth bounded domain such that ξi ∈ , i = , , . . . ,k, k ≥ , are different points, ≤ μi < μ̄ := (N–  ), L := – · – ∑k i=μi · |x–ξi| , η,λ,σ ≥ , a,a,a ∈ R,  < α, β < ∗ – , α + β = ∗. We work in the product space H ×H , where the space H :=H ( ) is the completion of C∞  ( ) with respect to the norm ( ∫ |∇ · | dx)   . In resent years many publications...