Ambrosetti–Prodi Type Results for Dirichlet Problems of Fractional Laplacian-Like Operators

被引：0
|
作者：
Anup Biswas
József Lőrinczi
机构：
[1] Indian Institute of Science Education and Research,Department of Mathematics
[2] Loughborough University,Department of Mathematical Sciences
来源：
Integral Equations and Operator Theory | 2020年 / 92卷
关键词：
Semi-linear nonlocal exterior value problem; Ambrosetti–Prodi problem; Viscosity solutions; Bifurcations; Fractional Schrödinger operator; Principal eigenvalues; Maximum principles; 35J60; 35J55; 58J55;
D O I：
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学科分类号：
摘要：
We establish Ambrosetti–Prodi type results for viscosity and classical solutions of nonlinear Dirichlet problems for fractional Laplace and comparable operators. In the choice of nonlinearities we consider semi-linear and super-linear growth cases separately. We develop a new technique using a functional integration-based approach, which is more robust in the non-local context than a purely analytic treatment.
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