Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multiple solutions for quasilinear elliptic problems with concave and convex nonlinearities

Federica Mennuni, Addolorata Salvatore

Abstract

We prove the existence of multiple signed bounded solutions for a quasilinear elliptic equation with concave and convex nonlinearities. For this, we use a variational approach in an intersection Banach space indroduced by Candela and Palmieri, and a truncation technique given by Garcia Azorero and Peral.

Multiple solutions for quasilinear elliptic problems with concave and convex nonlinearities

Abstract

We prove the existence of multiple signed bounded solutions for a quasilinear elliptic equation with concave and convex nonlinearities. For this, we use a variational approach in an intersection Banach space indroduced by Candela and Palmieri, and a truncation technique given by Garcia Azorero and Peral.
Paper Structure (4 sections, 8 theorems, 38 equations)

This paper contains 4 sections, 8 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Abstract setting and main result
  3. Existence of a local minimum of ${\cal J}$
  4. Existence of a mountain pass type critical point of ${\cal J}$

Key Result

Proposition 2.2

If $J \in {C}^{1}(X,\mathbb R)$ is bounded from below in $X$ and $(wCPS)_\beta$ holds at level $\beta ={\inf_{X} J \in \mathbb R}$, then $J$ attains its infimum, i.e., ${u}_0 \in X$ exists such that $J({u}_0)= \beta$ and $dJ(u_0)=0$.

Theorems & Definitions (20)

  • Definition 2.1
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Remark 2.4
  • Remark 2.5
  • Theorem 2.6
  • Theorem 2.7
  • Proposition 2.8
  • ...and 10 more