Existence and multiplicity of positive solutions for a class of nonlinear elliptic problems

Aghajani, Asadollah; Shamshiri, Jamile

doi:10.3906/mat-1107-23

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2015

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“…The most common approach is topological, for example Schauder fixed point theorem was used in [12], Schaefer fixed point theorem was employed in [14], Leray-Shauder degree theory was exploited in [4,5,25], fixed point index on cones was applied in [16,23] and continuation methods were used in [3]. Variational methods, making use of the Nehari manifold, have been used in [1,21], super and subsolution methods were applied in [7,11] and monotone techniques in [9].…”

Section: Introductionmentioning

confidence: 99%

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A topological approach to the existence and multiplicity of positive solutions of $(p, q)$-Laplacian systems

Infante

Maciejewski

Precup

2015

Dynamics of Partial Differential Equations

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In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational, quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.

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Section: Introductionmentioning

confidence: 99%

“…The multiplicity of solutions was studied in [1,21,25], nonexistence was investigated in [5,23,25], a priori estimates were given in [3,25], regularity results were obtained in [7] and qualitative properties of the solutions have been studied in [18].…”

Section: Introductionmentioning

confidence: 99%