Nontrivial solutions of a nonlinear heat flow problem via Sperner’s Lemma

Eigenvalue for a singular second order three-point boundary value problem

“…Motivated by the study of II'in and Moiseev, Gupta [6] studied certain three-point boundary value problems for nonlinear ordinary differential equations. Since then, more general nonlinear second-order three-point or mutipoint boundary value problems have been studied by many authors and obtained some results (see [7][8][9][10][11]). …”

Solvability of a nonlinear boundary value problem

“…Many of the results involving nonlocal boundary value problems are studied in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Using the Leray-Schauder nonlinear alternative some results on the existence of solutions for the equation (1.1) subject to the conditions u (0) = 0, u (1) = αu (η) can be found in [12,20].…”

“…In general nonlinearities that refer to source terms represent specific physical laws, in chemistry, for example, if f (t, u) = ug(u)e u−1 ε , then it represents Arrheninus law for chemistry reactions, where the positive parameter ε represents the activation energy for the reaction and the continuous function g represents the concentration of the chemical product, see [1]. The nonlocal conditions (1.2) arise in the study of the equilibrium states of a heated bar [17], in this situation two controllers at t = 0 and t = η alter the heat according to the temperatures detected by a sensor at t = 1.…”

“…Motived by a work of Guidotti and Merino [11] and using fixed point index theory or Sperner's Lemma, Infante and Webb in [5] studied the boundary conditions u ′ (0) = 0, σu ′ (1) + u(η) = 0 and Webb [20] provides explicit optimal constants for the problem. Infante and Webb [6], Palamides, Infante and Pietramala [17] and Fan and Ma [9] studied u…”

Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma

“…u  has been addressed by Palamides, Infante and Pietramala [17]. They approached the continuous nonlinearity by a sequence of locally Lipschitz functions and then each such a Lipschitz boundary value problem ensure the existence of a solution.…”