UNIQUENESS OF POSITIVE AND COMPACTON-TYPE SOLUTIONS FOR A RESONANT QUASILINEAR PROBLEM

被引：5

作者：

Anello, Giovanni ^{[1
]}

Vilasi, Luca ^{[1
]}

机构：

[1] Univ Messina, Dept Math & Comp Sci, Phys Sci & Earth Sci, Viale F Stagno Dalcontres 31, I-98166 Messina, Italy

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2017年 / 49卷 / 02期

关键词：

Quasilinear problem; resonant problem; positive solution; compacton-type solution; uniqueness; BOUNDARY-VALUE-PROBLEMS; P-LAPLACIAN;

D O I：

10.12775/TMNA.2016.090

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a one-dimensional p-Laplacian resonant problem with p-sublinear terms and depending on a positive parameter. By using quadrature methods we provide the exact number of positive solutions with respect to mu is an element of ]0,+infinity[. Specifically, we prove the existence of a critical value mu(1) > 0 such that the problem under examination admits: no positive solutions and a continuum of nonnegative solutions compactly supported in [0, 1] for mu is an element of ]0,mu(1)[; a unique positive solution of compacton-type for mu = mu(1) a unique positive solution satisfying Hopf's boundary condition for mu is an element of]mu(1),+infinity[.

引用

页码：565 / 575

页数：11

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