Multiple solutions for semilinear elliptic equations with nonlinear boundary conditions

Junichi Harada, Mitsuharu Otani

Research output: Contribution to journalArticle

Abstract

We consider the elliptic problem with nonlinear boundary conditions: Δu + bu = f (x, u) in Ω, - ∂ νu = {Pipe}u{Pipe} q-1u - g(u) on dΩ, where Ω is a bounded domain in ℝ n. Proving the existence of solutions of this problem relies essentially on a variational argument. However, since L q+1(∂Ω) ⊂ H 1(Ω) does not hold for large q, the standard variational method can not be applied directly. To overcome this difficulty, we use approximation methods and uniform a priori estimates for solutions of approximate equations.

Original language English 1-9 9 Electronic Journal of Differential Equations 2012 Published - 2012 Feb 23

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Uniform Estimates
Semilinear Elliptic Equations
Nonlinear Boundary Conditions
Multiple Solutions
A Priori Estimates
Variational Methods
Approximation Methods
Elliptic Problems
Existence of Solutions
Bounded Domain
Standards

Keywords

• Nonlinear boundary conditions

• Analysis

Cite this

In: Electronic Journal of Differential Equations, Vol. 2012, 23.02.2012, p. 1-9.

Research output: Contribution to journalArticle

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