Asymptotic behavior of solutions to a boundary value problem with mixed boundary conditions and friction law

Asymptotic Behavior of Energy Solutions to a Two Dimensional Semilinear Problem with Mixed Boundary Condition

Pergamon Asymptotic Behavior of Energy Solutions to a Two-dimensional Semilinear Problem with Mixed Boundary Condition

where: • f~ is a C °'1 and bounded domain in Rz; • 0f~ consists of two pieces F0 and F1, where the one-dimensional Hausdorff measure of F o is greater than 0; • F0 is smooth and F1 is piecewise smooth; • F0 and 1"1 are relatively closed in 0f~; • v is the unit outer normal of f~; • p is a large parameter. In this work, we shall only consider the least energy solutions, although the method can b...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

and Applied Analysis 3 In BVP 1.4 – 1.6 , it can be found that the boundary condition 1.5 is dependent on all the x a , x b , x′ a , and x′ b terms. First, existence and uniqueness of solutions of BVP 1.4 – 1.6 is established by combining the method of upper and lower solutions with LeraySchauder degree theory. Then, the general quasilinearization method is applied to construct the approximatio...

Existence of Positive Solutions of a Nonlinear Second-order Boundary-value Problem with Integral Boundary Conditions

In this article we prove the existence of at least one positive solution for a three-point integral boundary-value problem for a second-order nonlinear differential equation. The existence result is obtained by using Schauder’s fixed point theorem. Therefore, we do not need local assumptions such as superlinearity or sublinearity of the involved nonlinear functions.