6533b81ffe1ef96bd1278477

RESEARCH PRODUCT

Positive solutions for parametric singular Dirichlet(p,q)-equations

Nikolaos S. PapageorgiouCalogero VetroYoupei ZhangYoupei Zhang

subject

Dirichlet problemPure mathematicsApplied Mathematics010102 general mathematicsSingular termPerturbation (astronomy)Monotonic function01 natural sciencesDirichlet distribution010101 applied mathematicssymbols.namesakeNonlinear systemsymbols0101 mathematicsLaplace operatorAnalysisParametric statisticsMathematics

description

Abstract We consider a nonlinear elliptic Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f ( z , x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .

yearjournalcountryeditionlanguage
2020-09-01Nonlinear Analysis
https://doi.org/10.1016/j.na.2020.111882