On the bifurcation results for fractional Laplace equations
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DOI: 10.1002/mana.201600250
Abstract: In this paper, we consider the bifurcation problem for the fractional Laplace equation (−Δ)su=λu+f(λ,x,u)inΩ,u=0inRn∖Ω, where Ω⊂Rn,n>2s(0 read more here.
Keywords: bifurcation results; fractional laplace; results fractional; laplace equations ... See more keywords
Non-negative solutions to fractional Laplace equations with isolated singularity
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DOI: 10.1016/j.aim.2020.107329
Abstract: Abstract In this paper, we study singular solutions of linear problems with fractional Laplacian. First, we establish Bocher type theorems on a punctured ball via distributional approach. Then, we develop a few interesting maximum principles… read more here.
Keywords: solutions fractional; fractional laplace; negative solutions; laplace equations ... See more keywords
Existence results for critical growth Kohn-Laplace equations with jumping nonlinearities
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DOI: 10.1515/dema-2025-0130
Abstract: Abstract This article is concerned with the existence of nontrivial solutions to critical growth Kohn-Laplace equations with jumping nonlinearities. Or, more specifically, we consider the following Kohn-Laplace problem: − Δ H u = b u… read more here.
Keywords: existence; laplace equations; kohn laplace; equations jumping ... See more keywords
Infinitely many solutions for semilinear Δλ-Laplace equations with sign-changing potential and nonlinearity
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DOI: 10.1556/012.2017.54.4.1382
Abstract: In this paper, we prove the existence of infinitely many solutions for the following class of boundary value elliptic problems { − Δ λ u+V( x )u=f( x,u ),x∈Ω, u=0,x∈∂Ω, where Ω is a bounded… read more here.
Keywords: solutions semilinear; many solutions; infinitely many; sign changing ... See more keywords
Multi-Dimensional Analytic Functions for Laplace Equations and Generalized Cauchy–Riemann Equations
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DOI: 10.3390/math13081246
Abstract: A new concept of projective solution is introduced for the multi-dimensional Laplace equations. We project the field point onto a characteristic vector to obtain a projective variable, which can be used to reduce the Laplace… read more here.
Keywords: riemann equations; laplace equations; cauchy riemann; multi dimensional ... See more keywords