scholarly journals Multiplicity of positive solutions for a degenerate nonlocal problem with p-Laplacian

2021 ◽  
Vol 11 (1) ◽  
pp. 357-368
Author(s):  
Pasquale Candito ◽  
Leszek Gasiński ◽  
Roberto Livrea ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Value Problem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlocal Problem ◽  
Nonlinear Boundary Value Problem ◽  
Nonlocal Term ◽  
Number Of Solutions ◽  
Multiplicity Of Positive Solutions

Abstract We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the L q -norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of “positive bumps” of the degenerate term. The solutions are also ordered according to their L q -norms.

scholarly journals Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yansheng He ◽  
Mingzhe Sun ◽  
Chengmin Hou
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Value Problem ◽  
Multiple Positive Solutions ◽  
Order Difference ◽  
Nonlinear Boundary Value ◽  
Order Difference Equation

We consider a discrete fractional nonlinear boundary value problem in which nonlinear termfis involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

The exact number of solutions for the second order nonlinear boundary value problem

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Peter Somora
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Boundary Value Problem ◽  
Infinitely Many Solutions ◽  
Number Of Solutions ◽  
Root Functions ◽  
Exact Number ◽  
Nonlinear Boundary Value

AbstractA second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA, P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained by the root function method as well.

scholarly journals ON SOLUTIONS OF ONE 6‐TH ORDER NONLINEAR BOUNDARY VALUE PROBLEM

2008 ◽  
Vol 13 (3) ◽  
pp. 349-355 ◽  
Author(s):  
Tatjana Garbuza
Keyword(s):  
Boundary Value Problem ◽  
Partial Derivative ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Nonlinear Boundary Value Problem ◽  
Special Technique ◽  
Oscillatory Behaviour ◽  
Number Of Solutions ◽  
Nonlinear Boundary Value

A special technique based on the analysis of oscillatory behaviour of linear equations is applied to investigation of a nonlinear boundary value problem of sixth order. We get the estimation of the number of solutions to boundary value problems of the type x(6) = f(t, x), x(a) = A, x′ (a) = A 1, x″(a) = A 2, x′″(a) = A 3, x(b) = B, x′(b) = B1 , where f is continuous together with the partial derivative f′x which is supposed to be positive. We assume also that at least one solution of the problem under consideration exists.

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