Critical growth problems for ½-Laplacian in ℝ

p-Laplacian problems with critical Sobolev exponent

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.

N−laplacian Equations in Rn with Critical Growth

We study the existence of nontrivial solutions to the following problem: { u ∈ W 1,N (R ), u ≥ 0 and −div(| ∇u |N−2 ∇u) + a (x) | u |N−2 u = f(x, u) in R (N ≥ 2), where a is a continuous function which is coercive, i.e., a (x) → ∞ as | x |→ ∞ and the nonlinearity f behaves like exp ( α | u |N/(N−1) ) when | u |→ ∞.

Critical fractional p-Laplacian problems with possibly vanishing potentials

Article history: Received 8 April 2015 Available online 12 August 2015 Submitted by R.G. Durán

2 01 0 N - Laplacian equations in R N with subcritical and critical growth without the Ambrosetti - Rabinowitz condition

Let Ω be a bounded domain in R . In this paper, we consider the following nonlinear elliptic equation of N -Laplacian type: (0.1) { −∆Nu = f (x, u) u ∈ W 1,2 0 (Ω) \ {0} when f is of subcritical or critical exponential growth. This nonlinearity is motivated by the Moser-Trudinger inequality. In fact, we will prove the existence of a nontrivial nonnegative solution to (0.1) without the Ambrosett...

The Method of Subsuper Solutions for Weighted p(r)-Laplacian Equation Boundary Value Problems