Positive solutions of critical quasilinear elliptic equations in RN

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F99%3A00042035" target="_blank" >RIV/49777513:23520/99:00042035 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Positive solutions of critical quasilinear elliptic equations in RN

Original language description

We consider the existence of positive solutions of (1) -Delta_pu=lambda g(x)|u|^{p-2}u+alpha h(x)|u|^{q-2}u+f(x)|u|^{p^*-2}u in R^N where lambda,alphain R, 1<p<N, p^*=Np/(N-p), the critical Sobolev exponent, and 1<q<p^*,qneq p. Let lambda^+_1>0 bthe principal eigenvalue of (2) -Delta_pu=lambda g(x)|u|^{p-2}u in R^N, int_{R^N} g(x)|u|^p>0, with u^+_1>0 the associated eigenfunction. We prove that, if int_{R^N} f|u^+_1|^{p^*}<0, int_{R^N}h|u^+_1|^q>0 if 1<q<p and int_{R^N}h|u^+_1|^q<0 ip<q<p^*, then there exist lambda^*>lambda^=_1 and alpha^*>0, such that for lambda in[lambda^+_1,lambda^*) and alpha in[0,alpha^*), (1) has at least one positive solution.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GA201%2F97%2F0395" target="_blank" >GA201/97/0395: Topological and variational methods for nonlinear boundary value problems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

1999

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematica Bohemica

ISSN

08627959

e-ISSN

—

Volume of the periodical

Roč.^124

Issue of the periodical within the volume

č.^2 - 3

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

18

Pages from-to

—

UT code for WoS article

—

EID of the result in the Scopus database

—