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The Existence of Solutions for a Semilinear Abstract Dirichlet Problem
-
Marek Galewski
Published/Copyright:
March 4, 2010
Abstract
We provide a new variational principle and duality for the problem
𝐿𝑢 = ∇𝐺(𝑢),
where 𝐿 is selfadjoint and ∇𝐺 is a gradient mapping such that 𝐺 satisfies superquadratic growth conditions. The results obtained can be applied to Dirichlet problems for both ordinary and partial differential equations.
Received: 2003-11-05
Revised: 2004-01-08
Published Online: 2010-03-04
Published in Print: 2004-June
© Heldermann Verlag
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Articles in the same Issue
- Maximal Subgroups of Some Classes of Semigroups of Binary Relations
- Additive Surjections Preserving Rank One and Applications
- Some Families of Generating Functions for the Bessel and Related Functions
- On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory
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- Noncommutative Symplectic Foliation, Bott Connection and Phase Space Reduction
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- On Absolutely Nonmeasurable Additive Functions
- On Higher Order Functional Differential Equations with Property A
- On the Behavior of Solutions of Linear Neutral Integrodifferential Equations with Unbounded Delay
- Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions
- A Sharp Endpoint Estimate for a Multilinear Littlewood–Paley Operator
- On an Initial-Boundary Value Problem for a Fourth Order Composite Equation with Bilaplacian
- An Application of Independent Families of Sets to the Measure Extension Problem
- Oscillation Results for Second Order Self-Adjoint Matrix Differential Systems
