On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions

DOI10.1007/BF01459750zbMath0790.35038MaRDI QIDQ1322091

Zhongxin Zhao, Ruth J. Williams, Zhen-Qing Chen

Publication date: 26 June 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165185

zbMATH Keywords

Schauder's fixed point theoremDirichlet boundary conditionssemilinear elliptic equationconformal deformation of metricsexistence of positive continuous solutionsimplicit probabilistic representation

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Brownian motion (60J65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions ⋮ Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems ⋮ Existence of positive bounded solutions of semilinear elliptic problems ⋮ The boundary growth of superharmonic functions and positive solutions of nonlinear elliptic equations ⋮ On the existence of positive solutions of singular nonlinear elliptic equations with Dirichlet boundary conditions ⋮ Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains ⋮ Limits at infinity of superharmonic functions and solutions of semilinear elliptic equations of Matukuma type ⋮ Estimates on the Green Function and Existence of Positive Solutions of Nonlinear Singular Elliptic Equations ⋮ BOUNDARY BEHAVIOR OF SUPERHARMONIC FUNCTIONS SATISFYING NONLINEAR INEQUALITIES IN A PLANAR SMOOTH DOMAIN

Cites Work

• A probabilistic approach to one class of nonlinear differential equations
• Green's functions for the Schrödinger equation with short-range potentials
• On the existence of positive solutions of nonlinear elliptic equations -- a probabilistic potential theory approach
• On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions
• Schrödinger semigroups
• Solving Semilinear Partial Differential Equations With Probabilistic Potential Theory
• Conditional Gauge and Potential Theory for the Schrodinger Operator
• An Exterior Dirichlet Problem with Applications to Some Nonlinear Equations Arising in Geometry
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