Existence results for nonlinear boundary value problems

EXISTENCE RESULTS FOR NONLINEAR IMPULSIVE qk-INTEGRAL BOUNDARY VALUE PROBLEMS

u(T ) = ∑m i=0 ∫ ti+1 ti g(s, u(s)) dqis, where Dqk are qk-derivatives (k = 0, 1, 2, . . . ,m), f, g ∈ C(J ×R, R), Ik ∈ C(R,R), J = [0, T ](T > 0), 0 = t0 < t1 < · · · < tk < · · · < tm < tm+1 = T , J ′ = J\{t1, t2, . . . , tm}, and ∆u(tk) = u(t + k ) − u(t − k ), u(t + k ) and u(t − k ) denote the right and the left limits of u(t) at t = tk (k = 1, 2, . . . ,m) respectively. The study of q-dif...

Existence and multiplicity results for nonlinear boundary value problems

This paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations. By using bifurcation and fixed point index theories in the frame of approximation arguments, the criteria of the existence, multiplicity and nonexistence of positive solutions are established. c © 2007 Elsevier Ltd. All rights reserved.

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions

Existence Results for Nonlinear Boundary-value Problems with Integral Boundary Conditions

In this paper, we investigate the existence of solutions for a second order nonlinear boundary-value problem with integral boundary conditions. By using suitable fixed point theorems, we study the cases when the right hand side has convex and nonconvex values.