Summary
We consider the semilinear boundary value problem for pseudo differential operators generating symmetric Dirichlet forms. Using a variational approach we establish the existence of solutions under some growth assumptions on the nonlinearity. We also develop a certain truncation technique based on the specific properties of Dirichlet forms. Such technique allows us to obtain results about existence of bounded positive solutions and to relax growth conditions on the nonlinearity.
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Dedicated to Alfonso Vignoli on the occasion of his 60th birthday
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Jacob, N., Moroz, V. (2000). On the Semilinear Dirichlet Problem for a Class of Nonlocal Operators Generating Dirichlet Forms. In: Appell, J. (eds) Recent Trends in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 40. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8411-2_18
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DOI: https://doi.org/10.1007/978-3-0348-8411-2_18
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9556-9
Online ISBN: 978-3-0348-8411-2
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