Solving Semilinear Partial Differential Equations With Probabilistic Potential Theory

DOI10.2307/2000305zbMath0577.60073OpenAlexW4240143509MaRDI QIDQ3698015

Joseph Glover, Patrick J. McKenna

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000305

zbMATH Keywords

semilinear equationelliptic differential operatordual Markov process

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Probabilistic potential theory (60J45)

Related Items (7)

On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions ⋮ Existence of positive bounded solutions of semilinear elliptic problems ⋮ Probabilistic approach to semilinear and generalized mixed boundary value problems ⋮ Positive Solutions of Systems of Semilinear Elliptic Equations: The Pendulum Method ⋮ On the multiplicity of the solution set of some nonlinear boundary value problems—II ⋮ Solving semilinear differential equations by probabilistic methods ⋮ On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions

Cites Work

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• Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
• Markov processes: Ray processes and right processes
• Semi-linear second-order elliptic equations in \(L^1\)
• Multiplicative functionals of dual processes
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Nonnegative Solutions for Weakly Nonlinear Elliptic Equations

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