Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent
Abstract In this work, we are interested in considering the following nonlocal problem − a + b ∫ Ω | ∇ u | 2 d x Δ u = μ | u | 2 ∗ − 2 u + λ | u | q − 2 u , x ∈ Ω , u = 0 , x ∈ ∂ Ω , where Ω ⊂ R N ( N ≥ 4 ) is a smooth bounded domain, a ≥ 0 , b > 0 , 1 q 2 , μ , λ > 0 and 2 ∗ = 2 N N − 2 is the critical Sobolev exponent. By using the variational method and the critical point theorem, some existence and multiplicity results are obtained.
Positive solutions for a nonlocal Schrödinger-Newton system involving critical nonlinearity
Abstract In this paper, we study the critical Schrodinger–Newton system with a nonlocal term, and establish the existence of multiple positive solutions via using variational method.
Water Quality Aspects of Irrigation and Drainage: Past History and Future Challenges for Civil Engineers
This paper presents a brief history of irrigation and drainage related to ASCE activities on its Jubilee. This paper discusses legislation and policies that affect irrigation and drainage practices, water quality constituents of increasing concern in irrigation and drainage practices, and presents a prognosis on the future of declining freshwater resources available for irrigated agriculture and growing water quality problems in irrigation and drainage. Civil engineers in ASCE’s Irrigation and Drainage Division have compiled an 80-year history of highly meritorious service and accomplishments. In the next millennium, civil engineers will face a formidable challenge in managing and protecting the precious freshwater resources in the U.S.