Extremal solutions for nonlinear functional -Laplacian impulsive equations

Anti-periodic Boundary Value Problems of <i>φ</i>-Laplacian Impulsive Differential Equations

“…Usually, p-Laplacian operator is replaced by abstract and more general version ϕ-Laplacian operator, which lead to clearer expositions and a better understanding of the methods which ware employed to derive the existence results (see [12,13]). Recently, Cabada and Tomecek [4] focussed on the ϕ-Laplacian differential equations (1) subject to impulsive functions (2) with non-local boundary conditions…”

“…Later, the paper [6] generalize the problem of [4] and considered a more general ϕ-Laplacian differential equations…”

“…After make a study of the monotonicity of the boundary condition functions in [4,6,8], we found that their boundary problems didn't include the anti-periodic boundary condition problems.…”

“…As far as we known, although the papers [4,6,8] study such a general ϕ-Laplacian problems with nonlinear boundary conditions, but its didn't contain the anti-periodic problems. Besides, there are few dependent references for studying the ϕ-Laplacian impulsive functional differential equations with anti-periodic boundary condition.…”

The Method of Subsuper Solutions for Weighted -Laplacian Equation Boundary Value Problems

“…But if min r∈ 0,1 p r ≤ q r ≤ max r∈ 0,1 p r , one can see that the corresponding functional is neither coercive nor satisfying Palais-Smale conditions, the results on this case are rare. There are many papers on the existence of solutions for p-Laplacian boundary value problems via subsuper solution method see [20][21][22][23][24] . But results on the sub-super-solution method for p x -Laplacian equations and systems are rare.…”