In a Quercetum petraeae-cerris forest in northeastern Hungary, we examined effects of litter input alterations on the quantity and quality soil carbon stocks and soil CO 2 emissions. Treatments at the Síkfőkút DIRT (Detritus Input and Removal Treatments) experimental site include adding (by doubling) of either leaf litter (DL) or wood (DW) (including branches, twigs, bark), and removing all aboveground litter (NL), all root inputs by trenching (NR), or removing all litter inputs (NI). Within 4 years we saw a significant decrease in soil carbon (C) concentrations in the upper 15 cm for root exclusion plots. Decreases in C for the litter exclusion treatments appeared later, and were smaller than declines in root exclusion plots, highlighting the role of root detritus in the formation of soil organic matter in this forest. By year 8 of the experiment, surface soil C concentrations were lower than Control plots by 32% in NI, 23% in NR and 19% in NL. Increases in soil C in litter addition treatments were less than C losses from litter exclusion treatments, with surface C increasing by 12% in DL and 6% in DW. Detritus additions and removals had significant effects on soil microclimate, with decreases in seasonal variations in soil temperature (between summer and winter) in Double Litter plots but enhanced seasonal variation in detritus exclusion plots. Carbon dioxide (CO 2 ) emissions were most influenced by detritus input quantity and soil organic matter concentration when soils were warm and moist. Clearly changes in detritus inputs from altered forest productivity, as well as altered litter impacts on soil microclimate, must be included in models of soil carbon fluxes and pools with expected future changes in climate.

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Forest vegetation and soils have been suggested as potentially important sinks for carbon (C) with appropriate management and thus are implicated as effective tools in stabilizing climate even with increasing anthropogenic release of CO . Drought, however, which is often predicted to increase in models of future climate change, may limit net primary productio (NPP) of dry forest types, with unknown effects on soil C storage. We studied C dynamics of a deciduous temperate forest of Hungary that has been subject to significant decreases in precipitation and increases in temperature in recent decades. We resampled plots that were established in 1972 and repeated the full C inventory by analyzing more than 4 decades of data on the number of living trees, biomass of trees and shrubs, and soil C content. Our analyses show that the decline in number and biomass of oaks started around the end of the 1970s with a 71% reduction in the number of sessile oak stems by 2014. Projected growth in this forest, based on the yield table's data for Hungary, was 4.6 kg C/m . Although new species emerged, this new growth and small increases in oak biomass resulted in only 1.9 kg C/m increase over 41 years. The death of oaks increased inputs of coarse woody debris to the surface of the soil, much of which is still identifiable, and caused an increase of 15.5%, or 2.6 kg C/m , in the top 1 m of soil. Stability of this fresh organic matter input to surface soil is unknown, but is likely to be low based on the results of a colocated woody litter decomposition study. The effects of a warmer and drier climate on the C balance of forests in this region will be felt for decades to come as woody litter inputs decay, and forest growth remains impeded.

We study the nonlinear elliptic equation Δu(x) + a(x)u(x) = g(x)f(u(x)) on the Sierpinski gasket and with zero Dirichlet boundary condition. By extending a method introduced by Faraci and Kristály in the framework of Sobolev spaces to the case of function spaces on fractal domains, we establish the existence of infinitely many weak solutions.

This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the field, with examples and exercises suitable for graduate students entering research. The method of presentation will appeal to readers with diverse backgrounds in functional analysis, differential geometry and partial differential equations. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. Since much of the material has a strong geometric flavor, the authors have supplemented the text with figures to illustrate the abstract concepts. Its extensive reference list and index also make this a valuable resource for researchers working in a variety of fields who are interested in partial differential equations and functional analysis.

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Dedicated to Professor Gheorghe Moroşanu on the occasion of his 65 th birthday.Abstract. In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calculus of variations, we establish uniqueness, location and rigidity results for singular Poisson equations involving the Finsler-Laplace operator on Finsler-Hadamard manifolds having finite reversibility constant.

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