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We give some expansion formulas and the Kelvin principle for solutions of a class of iterated equations of elliptic type
    			                    
    			                 
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    			                    
                                       
We consider the following problem:  where Φ: Ω ⊂  → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
    			                    
    			                 
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    			                    
                                       
We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point  of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...
    			                    
    			                 
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    			                    
                                       
We study the linearized water-wave problem in a bounded domain (e.g. a
finite pond of water) of , having a cuspidal boundary 
irregularity created by a submerged body. In earlier publications the 
authors discovered that
in this situation the spectrum of the problem may contain a 
continuous component in spite of the boundedness of the domain. 
Here, we proceed to impose and study radiation conditions at a point  
of the water surface, where
a submerged body touches the surface 
(see Fig. 1)....
    			                    
    			                 
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    
    		            
    		                
    		                
    		                
    			                
    		                
    		                
    		            
    			    			
    			 
 
    			
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