Search results for "subsolution-supersolution"

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Systems of quasilinear elliptic equations with dependence on the gradient via subsolution-supersolution method

2017

For the homogeneous Dirichlet problem involving a system of equations driven by \begin{document}$(p,q)$\end{document} -Laplacian operators and general gradient dependence we prove the existence of solutions in the ordered rectangle determined by a subsolution-supersolution. This extends the preceding results based on the method of subsolution-supersolution for systems of elliptic equations. Positive and negative solutions are obtained.

System of elliptic equationDirichlet problemApplied Mathematics010102 general mathematicsMathematical analysisMathematics::Analysis of PDEsSystem of linear equations01 natural sciences(pq)-Laplacian010101 applied mathematicsSubsolution-supersolution and gradient dependenceSettore MAT/05 - Analisi MatematicaHomogeneousDiscrete Mathematics and CombinatoricsRectangle0101 mathematicsLaplace operatorAnalysisDirichlet problemMathematicsDiscrete & Continuous Dynamical Systems - S
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Location of solutions for quasi-linear elliptic equations with general gradient dependence

2017

Existence and location of solutions to a Dirichlet problem driven by $(p,q)$-Laplacian and containing a (convection) term fully depending on the solution and its gradient are established through the method of subsolution-supersolution. Here we substantially improve the growth condition used in preceding works. The abstract theorem is applied to get a new result for existence of positive solutions with a priori estimates.

subsolution-supersolutionGradient dependenceApplied Mathematics010102 general mathematicsMathematical analysisMathematics::Analysis of PDEs$(pQuasi-linear elliptic equationq)$-laplacian01 natural sciences010101 applied mathematics(p q)-laplacian; Gradient dependence; positive solution; Quasi-linear elliptic equations; subsolution-supersolution; Applied Mathematicspositive solutionSettore MAT/05 - Analisi MatematicaQA1-939Quasi linear0101 mathematicsquasi-linear elliptic equationsMathematics(p q)-laplacianMathematics
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