in this paper, we study the nehari manifold and its application on the following navier boundary valueproblem involving the p-biharmonic          0, on( ) 1 ( , ) , in , 2*2u uf x u u upu u p q where  is a bounded domain in rn with smooth boundary  . we prove that the problem has atleast two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset o...

We use variational methods to study the asymptotic behavior of solutions of p-Laplacian problems with nearly subcritical nonlinearity in general, possibly non-smooth, bounded domains.

where Ω ⊂ R(N ≥ 4) is an open bounded domain with smooth boundary, β > 0, 0 ∈ Ω, 0 ≤ s < 2, 2∗(s) := 2(N − s) N − 2 is the critical Hardy-Sobolev exponent and, when s = 0, 2∗(0) = 2N N − 2 is the critical Sobolev exponent, 0 ≤ μ < μ := (N − 2) 4 . In [1] A. Ferrero and F. Gazzola investigated the existence of nontrivial solutions for problem (1.1) with β = 1, s = 0. In [2] D. S. Kang and S. J. ...

In this paper, we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nerahi manifold and by exploring some properties of the best Hardy-Sobolev constan...

‎We present a Picone's identity for the‎ ‎$mathcal{A}_{p(x)}$-Laplacian‎, ‎which is an extension of the classic‎ ‎identity for the ordinary Laplace‎. ‎Also‎, ‎some applications of our‎ ‎results in Sobolev spaces with variable exponent are suggested.

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...