## Differential and Integral Equations

### Non-uniformly elliptic equations with non-uniformly $p$-superlinear nonlinearities

Nguyen Quang Huy

#### Abstract

The purpose of this paper is to study the non-uniformly elliptic equations with non-uniformly $p$-superlinear nonlinearities satisfying sets of other nonuniform conditions. In particular, we weaken the well-known Ambrosetti-Rabinowitz condition. By introducing the notion of pseudo-uniform convexity, we complete the studies in [5], [10] for non-uniformly p-Laplacian problems with $1 < p < 2$. We are able to prove the existence of nontrivial, non-negative, non-positive solutions.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 9/10 (2014), 977-1000.

Dates
First available in Project Euclid: 1 July 2014

Huy, Nguyen Quang. Non-uniformly elliptic equations with non-uniformly $p$-superlinear nonlinearities. Differential Integral Equations 27 (2014), no. 9/10, 977--1000. https://projecteuclid.org/euclid.die/1404230053