Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function

Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight

In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Morse theory and the Ljusternik-Schnirelmann category, we investigate how the coefficient h(x) of the critical nonlinearity affects the number of positive solutions of that problem and we get some results as regards the...

Multiplicity of positive solutions for critical singular elliptic systems with sign - changing weight function ∗

In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.

Multiple results for critical quasilinear elliptic systems involving concave-convex nonlinearities and sign-changing weight functions∗

This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems    −4pu = λa1(x)|u|q−2u + b(x)Fu(u, v), in Ω, −4pv = λa2(x)|v|q−2v + b(x)Fv(u, v), in Ω, u = v = 0, on ∂Ω, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω; 1 < q < p < N , p∗ = Np N−p ; 4pw = div(|∇w|p−2∇w) denotes the p-Laplacian operator; λ > 0 is a positive pa...

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

Multiple Solutions and a Sign-Changing Solution for Semi-Linear Elliptic Problems with Resonance