Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent

Multiple Positive Solutions for Equations Involving Critical Sobolev Exponent in R N

This article concerns with the problem ?div(jruj m?2 ru) = hu q + u m ?1 ; in R N : Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of > 0 such that there are at least two non-negative solutions for each in (0;).

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities

and Applied Analysis 3 When a 0, we set s dp∗ 0, d and t bp∗ 0, b , then 1.1 is equivalent to the following quasilinear elliptic equations: −div ( |∇u|p−2∇u ) − μ |u| p−2u |x| |u|p t −2u |x| λ |u|q−2u |x| in Ω, u 0 on ∂Ω, 1.7 where λ > 0, 1 < p < N, 0 ≤ μ < μ N − p /p , 0 ≤ s, t < p, 1 ≤ q < p and p∗ t p N − t / N − p . Such kind of problem relative with 1.7 has been extensively studied by many...

Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent

where λ > 0 is a parameter, κ ∈ R is a constant, p = (N + 2)/(N − 2) is the critical Sobolev exponent, and f(x) is a non-homogeneous perturbation satisfying f ∈ H−1(Ω) and f ≥ 0, f ≡ 0 in Ω. Let κ1 be the first eigenvalue of −Δ with zero Dirichlet condition on Ω. Since (1.1)λ has no positive solution if κ ≤ −κ1 (see Remark 1 below), we will consider the case κ > −κ1. Let us recall the results f...

On Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...