Multiple Positive Solutions For a Class of Nonlinear Elliptic Equations

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Shenghua Weng ◽  
Yongqing Li
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nonlinear Elliptic Equations ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractThis paper deals with a class of nonlinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results.

scholarly journals Multiple positive solutions of Strum-Liouville equations with singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Zenggui Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity

The existence of multiple positive solutions for Strum-Liouville boundary value problems with singularities is investigated. By applying a fixed point theorem of cone map, some existence and multiplicity results of positive solutions are derived. Our results improve and generalize those in some well-known results.

scholarly journals Some notes on the method of moving planes

1992 ◽  
Vol 46 (3) ◽  
pp. 425-434 ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Nonlinear Elliptic Equations ◽  
Smoothness Condition ◽  
Plane Method ◽  
Nonlinear Elliptic ◽  
Method Of Moving Planes ◽  
Moving Planes

In this paper, we obtain a version of the sliding plane method of Gidas, Ni and Nirenberg which applies to domains with no smoothness condition on the boundary. The method obtains results on the symmetry of positive solutions of boundary value problems for nonlinear elliptic equations. We also show how our techniques apply to some problems on half spaces.

scholarly journals Multiplicity results for some nonlinear elliptic problems

2004 ◽  
Vol 76 (2) ◽  
pp. 247-268
Author(s):  
Kuan-Ju Chen
Keyword(s):  
Ground State ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Ground State Solution ◽  
State Solution ◽  
Energy Solution ◽  
Nonlinear Elliptic Problems ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Half Strip

AbstractIn this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.

ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS

2010 ◽  
Vol 08 (02) ◽  
pp. 185-197 ◽  
Author(s):  
F. J. S. A. CORRÊA ◽  
J. V. GONCALVES ◽  
ANGELO RONCALLI
Keyword(s):  
Boundary Conditions ◽  
Fixed Points ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Compact Operators ◽  
Schmidt Method ◽  
Navier Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

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