The existence of three solutions for elliptic Neumann problems with a perturbed nonlinear term depending on two real parameters is investigated. Our approach is based on variational methods.

/pdf/multiplicity-results-for-a-perturbed-elliptic-neumann-q1sx472tmg.pdf

Multiplicity Results for a Perturbed Elliptic Neumann Problem

Using perturbation results on the sums of ranges of nonlinear accretive mappings of Calvert and Gupta [B.D. Calvert, C.P. Gupta, Nonlinear elliptic boundary value problems in L^p-spaces and sums of ranges of accretive operators, Nonlinear Anal. 2 (1978) 1-26], we present some abstract existence results for the solutions of nonlinear Neumann boundary value problems involving the generalized p-Laplacian operator. The equation discussed in this paper and the method used extend and complement some of the previous work.

Existence of solutions to nonlinear Neumann boundary value problems with generalized p-Laplacian operator

Consider { (oulp-2u')' AlUlp-2U + f(X), x E (0, 1), tu(0) = /3u'(0), u'(1) = 0, where p > 1 and /3 E iR U {oo} and let Al be the principal eigenvalue of the problem with f(x) 0 O. For A = Al, we discuss for which values of p and /3 the Fredholm alternative holds.

/pdf/on-the-fredholm-alternative-for-the-p-laplacian-4u8xl9iay2.pdf

On the Fredholm alternative for the $p$-Laplacian

In this paper we introduce a notion of asymptotic almost-equivalence of two evolution systems and provide simple tests that guarantee that two evolution systems have the same qualitative asymptotic properties. In this way we are able to unify and extend many previously known results and also to understand what is behind equally behaved systems. In particular, we establish convergence, ergodic convergence and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits.

/pdf/asymptotic-almost-equivalence-of-lipschitz-evolution-systems-2d2csc628q.pdf

Asymptotic almost-equivalence of Lipschitz evolution systems in Banach spaces

The applications of theories of accretive operators to nonlinear elliptic boundary value problems in Lp-spaces

The applications of sums of ranges of accretive operators to nonlinear equations involving the P -Laplacian operator

Some mapping theorems involving the perturbations of m -accretive operators

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The applications of theories of accretive operators to nonlinear elliptic boundary value problems in Lp-spaces

The applications of sums of ranges of accretive operators to nonlinear equations involving the P -Laplacian operator

Some mapping theorems involving the perturbations of m -accretive operators